Turning off tube preamp first sends solid state amp into protection?

You Never do this ,it creates a surge . Allways do the Opposite 
with tube gear preamp on first until stable ,30-40 seconds then amplifier, shut off in reverse order you can blow your tweeter in your speaker also you hear a pop or thump.  solid state pre not an issue ,or a stand by . But this is a good rule of thumb.

I'm glad this came up. I'm a newbie at this. I have an AR LS-16 (tube) and a SS Proceed HPA2 amp.

The pre-amp has a 45 second warm-up timer before anything will function.

The amp has two buttons. A tiny off/on button and a large large round 'standby' button.

When I turn the system on I turn the LS pre-amp on first then immediately turn on the amp which stays in standby mode until you hit the standby button. The are no audible clicks on pops through the speakers but you can hear clicks in both components.

When I turn the system off, I put the amp in standby then turn it off. Then I turn the LS pre-amp off. This way there are no audible clicks from the speakers.

Does this sound right?

Many tube amp designs shunt the outputs during shut-down.  Some amps will see this as a shorting of the input.

 I definitely agree with what some of the other folks have said here about operational sequence.  I always try to remember this about my main amplifier: “last on, first off. “
 
 I switch on everything else first and wait until it is fully powered on and only then turn on my main amplifier. When I’m done listening I switch the main amplifier off first before I switch off the other gear. 

 I hope this helps. 

The turn on/off order has nothing to do with tube vs. solid state. You turn on the pre-amp and sources before the power amp because the amp can’t send any of their on/off noise to the speakers until it is on. And you turn off the amp first for the same reason.