I should wait for 15 minutes before I turn them back on to avoid damaging the amps or tubes.
On my ARC tube amp I wait at least 5 minutes. YMMV.
Should I always wait before switching a warm, but powered off amp back on? Is the reverse also an issue? Can I turn off a tube amp too quickly after turning it on?
Turning off a power amp is not a problem. Turning it back on too soon after shutdown can do harm to the amp or possibly your speakers.
The main reason you should wait a reasonable time before powering back up a power amp is to allow the electrolytic caps in the power supply to discharge. Failure to do so could damage the power supply or possibly damage your speakers from a loud transient spike thump.
If you have ever experienced a loss of mains AC power caused by the Utility Power Company for 10 or 15 seconds and then come back on you more than likely have experienced the loud thump sound through your speakers.