No, it isn't supposed to work that way. Although amps are usually wired with the positive directly to the vehicle battery, they aren't supposed to turn on unless power is supplied on the remote wire.
The problem is most likely in either the head unit or one of the amps. And if not corrected, the amps will sooner or later, completely drain the battery.
First see if it works properly with just one amp connected. Remove the remote turn-on from 1 amp at a time and test with the vehicle and head unit off and then on. If the problem is still there with just one amp connected, either the head unit is at fault or the remote wire is picking up 12V somewhere along it's path to the amps. Make sure you have it connected to the right wire on the Kenwood. Every Kenwood I've seen uses blue/white for the remote wire.
If both amps work OK separately, one of the amps is causing the problem. You may be able to correct it by using a relay to electrically separate the turn-on signal for each amp. You'll need a "double-throw, single-throw" type of relay. Here's a link to the Basic Car Audio Electronics web site that details the connections http://www.bcae1.com/
. Connect the remote wire coming from the head unit to one side of the relay coil and ground the other side. Bring 12V positive from an "accessory" lead that is hot only when the ignition is in either the "ON" or "ACCESSORY" positions to one side of both sets of relay contacts (it doesn't matter which side). Connect the other sides of the relay contacts, one to each amp turn-on connector.
Hope this helps.