Yea, echoing many of the above, many amps have a time-delayed muting switch that kills the feed during powering on / off in order to avoid this issue. Some don't, however, and you get to listen to the nasty bits as they ramp up or down.
Bryston, for example, had a batch of amps that went out with a muting switch which failed after a number of years. Once it went, you knew it. Particularly at powering down. Kinda sounded like they were trying to tear the speakers in half as the stored power bled through the feeds as you powered down. It was a known issue, however, and was fixed for free (ah, Bryston service really is second to none) with no fuss nor muss.
Definitely sounds like what you're hearing, though. I'd check with the manufacturer. If it's something the amps do, then nothing to worry about. If, however, they're designed with a muting switch which isn't doing it's job -- then it may be time to think about having that looked at.
And I definitely agree with Joe, as a general rule of thumb, the amp is the first off and the last on in order to avoid passing such artifacts to the speakers in the event other items in the chain pull similar shenanigains. Best of luck.