I've played both monkey islands multiple times and I don't remember any time limit. Everything went at the speed of plot.
(Among many other ways, which you can find here: https://www.maniacmansionfan.50webs.com/waystolose.html)
https://web.archive.org/web/20240529033339/https://www.mania...
It's still a bizarrely high-pressure moment built into a game that otherwise has no such mechanics. I always hated coming to it.
It would have been at least as easy to tie the disintegration of the mugs to scene transitions, which would have eliminated the time pressure at no cost to the game.