According to the reminder text on one of the cards, time travel seems to be like proliferate for suspend counters, except you can either add or subtract from any suspended cards. Could be fun if all doctors are messing with when things happen in different ways. I can feel the timely-wimey shenanigans from here.
Oh shoot it’s because it’s each player and not each opponent. I didn’t realize that at first. Took your question for me to notice