After washer has stopped, it contunes to drip inside the tube

most likely washer in tap is worn.
https://www.youtube.com/watch?v=VyfL2wLqPbA
https://www.youtube.com/watch?v=yflwG8IkRO8
also note the comment in you tube about the rubber washer seal could be a cause.
https://www.youtube.com/watch?v=LV9HIEhr1G8

Try to follow these two you tube videos and see which one applies to your style of faucet.

Good luck.
How to change or tap washer to stop dripping tap or replace the type of...

How To Fix Dripping Tap Washer Change Plumbing Tips

nF--Washer tried to fill but was unsuccessful
maybe a faulty water valve

If not during a wash it is standing water.

Remove tube and check for cracks. If so, replace. Does/did the washer "walk"? May have rubbed the discharge tube and caused the leak.

Is the down pipe in a cold external wall? May be condensation from humid air hitting cold.

If the sound is the problem, attach a string to the drain pipe so water drips directly to side of vertical pipe.

Sounds like a professional needs to diagnose and repair/replace the water valves.

You might take it back to who ever changed the idle air control motor and ask them about it. They could have knocked the drain tube out, or plugged it to stop it from dripping on them or the floor.
You can try this...

Could be the drain tube is partially clogged. It is usually located on the fire-wall or down towards the floor pan under the car. It is usually close to where the A/C lines go thru the fire-wall. About 1/2 inch diameter sticking straight out but may have a 90 degree elbow pointing down.
Also, it's been extra hot and humid all over and moisture could be freezing inside the unit when on MAX A/C, then suddenly melting when switched to normal. This opens the outside air door and allows warm/hot air into the unit instead of recirculating the cold air inside the car. The drain may not be able to handle a large, sudden quantity of water.
Perform a "driveway" test. Open the hood, start engine and run the A/C on normal with the windows or doors open. Locate the drain tube by looking for water dripping. Once located twist 2 or 3 pipe cleaners together and verify the tube is clean. Then close the doors/windows and switch to MAX A/C. Check for water dripping. If it stops dripping, water is freezing inside and now you know why!

you need to clean out the diverter before replaceing with new washers and seats.

Water valve needs replacing. Determine which one by turning off either hot or cold at the wall and watching to see if drip stops.
Alternatively, just turn off the wall taps each time you finish washing.

Turn the water faucets off and listen for the drip to stop.
If the dripping noise stops,replace the water inlet valve on the washer were the hoses connect.
Enter your model number in the site referenced here for parts.

www.appliancepartspros.com