before the changed despot you could 100% pop him by zoning a bunch of dolls. Plenty of times i would agro an entire row and zone them and then the row would repop and despot would be in one of he cubbie holes. this doesn't really work anymore though with any NM's that I know of. sometimes zoneing and kill non PH i found to increase the pop time like ulli durring the 6 months that he was fucked up for if you rounded up the statues up there and and ran aroundn to lose hate or had a thf hide and lose hate ulli would never repop and from my experiance it would increase the time it took to pop him. every NM is different and you can't really say cause X Nm pops this way then Y NM will also.
I don't know if Despot's lotto is different, but he spawns claimed to whoever killed his PH.
unless the person who killed him is engadged to a new mob ether through auto-target or attacking a new one, then it will pop yellow cause person who kill PH has claim on a new mob.