When Peter was taken back by his father he was asleep for 3 days and had all sorts of drips and things to help him adjust - the same for Walternate when he crossed from his Universe. Also when Red verse Olivia wanted to come back she was told how dangerous it was, and all the experiments Walternate did on Olivia with the tank and drugs shows that their way of crossing was not as safe as he would have liked. Perhaps it would have been a little more believable if Red Olivia had taken a few days to adjust instead of going right back to work.
Of course there is no other Universe really, so they can make up anything they want to justify the story!
