Re:Cerebro on the fritz! Help!
This card definitely means that they physically go back to headquarters to "repair the computer for one turn". So, essentially the player who is at the receiving end of this card has to remove all of his/her X-Men from the Battle Zone and Deployment Area and then misses their next turn completely. And I think it's also obvious that they have to start the Battle all over again (if they choose to go back into that same Battle). It does not specifically say that they HAVE to go back into that same battle. I think that after the player misses their turn for one round, they then have the option to do whatever they want, whether that be to heal, start the battle over again, or start a battle against a different Evil Mutant. Your question about characters with Flight or Teleporting becomes irrelevant because of this last point.