I don’t mind the idea of a timer, since it makes for a sense of urgency. Hurry up, get in, get the loot, and get back out. And dying adds an extra level of urgency, b/c if it only ejected you at the end, then you’d still make it out with whatever loot you managed to score in that time. As @Vuhdo_Rin mentioned, people would just gear up for maximum tank, try to clear a room or two, and let themselves get sucked out with the loot they scored from those rooms.
However… I do think it’s funny that the Trig ships are supposed to be FROM those regions, and they can hang out in there all day long. But you fly one in there yourself, and you still have the time limit. So one thing I’d consider is adding a Role Bonus to them allowing for longer durations (if not unlimited duration) inside. Sure, that only applies to the Vedmak Cruiser right now, but maybe they’ll come out with Frig or BS pockets later?
And from that adaptation idea, we could also have a Trig Rig, or a Trig based Damage Control, which lets you extend the time for any ship. Sacrifice a bit of tank or something, for the ability to add a couple extra minutes to your Abyss fit.