Sounds a bit like one of the stages is getting a big pulse when the high voltage is applied, possibly due to a problem with the coupling capacitor circuit somewhere... I suspect a resistor from a grid to ground may have a loose connection.
What may be happening is that the capacitor has noplace to send the charge that it gets when the voltage rises.... and the result is a temporary DC offset which cuts off a tube and you hear the power supply "ripple" as hum.
After you play it for a bit, things can even out.
Do you notice any distortion right when you start playing? Especially if you don't wait for the hum to go away.
Yes I USED TO work for Ampeg...but I haven't forgotten everything.