My leviton countdown timer switch makes my bathroom exhaust fan rotate much more slowly than a regular switch. Why?

Leviton 6161 is shown on Leviton as 500 watt incandescent-only 4-level dimmer that cannot control a fan.
If this is a ceiling fan and light, then search for fan light dimmer, or fan control,

If this is bathroom fan-light installation, you are needing a countdown timer rated for both bulb and fan... which will require Neutral wire...
Different timer choices with manuals appear following link:
http://waterheatertimer.org/Countdown-timer-horsepower-ratings.html#Leviton

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Copy following link for instructions wiring single-pole timer.
http://waterheatertimer.org/How-to-wire-timers.html
http://waterheatertimer.org/Countdown-timer-horsepower-ratings.html

Leviton countdown timer model number is unknown.
Which timer has green lights? I thought the leds were red.
Add comment with wire colors on timer and fuller description of timer, and what the timer does.

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There are no repairs for electronic wall timers.
Timers have 1 year warranty against defects in workmanship. This sounds like the case here.

Try timer on different circuit and see if same malfunction appears.

Woods is rated for 1/4 HP and will handle bath fan, so load does not sound like a problem.
Timer worked before, so wiring is correct.
Power outages can knock out timers when the power turns on again and timer is exposed to surge.

View countdown timers:
Electronic Leviton 6200 series and Leviton LTB series are more robust than Woods.
Mechanical rotary-type timers have no electronics, and last many years without problems.
Buy locally: GE countdown timers are sold at Home Depot. Advantage of store-bought timer is hassle-free warranty: buy new timer and return defect timer in new package.
http://waterheatertimer.org/Countdown-timer-horsepower-ratings.html

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Question is not clear.
Add a comment and say specifically what timer you have and what type of switch(es) you want to control, and add what voltage you are working with and what color wires you have.

You posted under Leviton 6230 30-minute countdown timer.
Generally, a countdown timer is not considered a programmable timer since the countdown program is already inside the timer.
With countdown timer, you push a button that turns circuit ON, and after countdown expires, the circuit turns OFF.
http://waterheatertimer.org/Countdown-timer-horsepower-ratings.html#6230

Countdown timer can easily switch a contactor ON, and then turn it off after countdown expires.
http://waterheatertimer.org/H230A.html

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Countdown timers are made to work with bath fans.
Leviton countdown timers are stout product with 1HP rating.
http://waterheatertimer.org/Countdown-timer-horsepower-ratings.html#6200

It sounds like timer is bad.
Wiring sounds good. Make sure you don't have Load and Line wires reversed. Try reversing Load-Line wires and see what happens.
Another thing that affects electronic timers is line noise/interference. If replacement timer does same thing, then noise is suspect. Try timer on another circuit without fan. Try another brand timer. Update to newer LTB60 Leviton timer. Use cheap circuit tester from home center to check outlet on same circuit.

1) Leviton 6515 is incandescent only:
http://www.amazon.com/Leviton-6515M-I-2-5-10-15-Electronic-Incandescent/dp/B0007NOZDI

2) Below is list of countdown timers with horsepower rating so they work for fans:

GE15088 countdown timer is rated 3/4 hp
http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay

Intermatic spring wound countdown timers are rated for 2 horsepower
http://www.intermatic.com/products/timers/in-wall%20timers/decorator%20spring%20wound%20timers.aspx

Woods spring-wound countdown timer says bath/ ceiling fans, but doesn't give horsepower
http://waterheatertimer.org/pdf/Wood-59700-series--spring-wound.pdf
http://waterheatertimer.org/Woods-timers-and-manuals.html#countdown

Woods push-button countdown is 1/4 horsepower
http://www.amazon.com/Woods-59014-Decora-12-8-4-2-12-Hour/dp/B002C54GH4

Wattstopper RT50 at Grainger shows 1/6 horsepower rating
http://www.grainger.com/Grainger/WATT-STOPPER-Time-Switch-2HTE1?Pid=search

3) Following timers are NOT rated for fans:

Lutron MA-T51 countdown timer specifically says it cannot be used for motors.
http://www.amazon.com/Lutron-MA-T51-WH-Maestro-Countdown-Timer/dp/B001EFV1DA
http://www.lutron.com/TechnicalDocumentLibrary/0301041A.pdf

Pass and Seymour RT1 countdown does not show rating for horsepower, so this timer will probably not work for fan motor
http://www.homedepot.com/Electrical/h_d1/N-5yc1vZ1xg8Zarcd/

You posted under UPM programmable timers
Open following link to identify product and download manual
http://waterheatertimer.org/UPM-timers-and-manuals.html

Q1) Some UPM timers, and other brands, offer countdown feature in addition to regular programming.
So you choose between regular programming and countdown.
Countdown is for a bathroom fan for example.
Push the button and fan turns on for set amount of time.
After countdown is over, fan turns off automatically.

Q2) Yes all days of the week can be selected.
Set event 1 ON for all days.
Set event 1 OFF for all days.
Do not set more events unless you want more on-off events.

Q3) Switch position depends on model number.
Add a comment with model number to identify product and I will look at manual alongside you.
Or try the switch in different positions.

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Leviton countdown timers have additional wire that powers internal electronics.
Leviton timers have red-black-white-green wires (or blue-black-white-green wires)

1) Regular single pole switch has 2 insulated wires. One of these wires is Hot from breaker, and the other goes to Load (fan)
2) Timer green wire connects to bare ground as you know.
3) Hot from breaker connects to timer black wire.
4) Load wire connects to timer red (or blue) wire.

5) Located in back of box are white wires that are twisted together and covered with wire nut.
These are Neutral wires. Connect timer white to these wires. This will power timer electronics.
6) If box does not have Neutral wires described above, then connect timer white to bare ground along with timer green wire.

7) Turn power ON and try timer countdown.
If timer does not work, then reverse timer red and timer black wire.

8) If box does not have neutral wires: Image on link below shows similar Intermatic timer:
Image applies ONLY when Neutral is not available.
http://waterheatertimer.org/images/EI210-wiring-full.jpg

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You need "15 minute countdown timer" for a bath fan.

1) Following page shows selection of timer types and brands:
http://waterheatertimer.org/Countdown.html
There are push button electronic types and rotary dial types.

2) Easiest to wire is mechanical spring type countdown timer, FD series.
No electronics that can be affected by 'electric noise' on fan circuit.
Intermatic spring-wound last for years without problem.
http://www.electricsupplyonline.com/prod/intermatic-springwound_timers.php

http://www.electricsupplyonline.com/prod/intermatic-springwound_timers/fd15mc_w005485.php

3) Another reliable timer is GE 15088 sold at Home Depot.
Timer has preset for 20 minutes, not 15
http://www.homedepot.com/webapp/wcs/stores/

4) Amazon sells reliable 15 minute Intermatic electronic countdown:
http://www.1000bulbs.com/product/3293/ELEC-EI200LA.html?utm_source=SmartFeedAmazonProduct

5) Timex sells 15 minute spring wound countdown timer. Lower price is probably with reason since Timex are generally sold in drug store/dollar store rather than hardware/electric outlets.
http://www.amazon.com/Timex-Minute-Springwound-Countdown-Timer/dp/B00013K69Q

6) Spring wound timers connect easily to same wires that come off old fan switch.
Old switch has 2 insulated wires, connect them to either terminal on spring wound timer.

7) Electronic timers are wired differently:
Instructions for wiring electronic timers appears on following link:
http://waterheatertimer.org/GE-timers-and-manuals.html#15088

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The Leviton 6230 is a countdown timer with maximum time of 30 minutes.
The other times are 15minutes, 5minutes and 3minutes.
The timer has a manual override.
Push the bottom button and the timer works like a switch.

Leviton also make the 6260 countdown ... with 10-20-30-60minute times.