OK, I'm thinking:
-Maybe there's 5 Psysquids. To prevent bugs in the system, I mean. Because nothing good can occur if a Psysquid hit his own button. So in each reality there's 4 buttons but not the one addressing the Psysquid native to that reality. So our Psysquid is not Yellow King nor Nihilism nor Conflagrate nor Sleeper, he would be something else.
-Yellow King Psysquid said he was in the temple the moment the change happened. So it must be required that both Psysquids are on the temple pressing each other's buttons (Yellow king pressed Regular Psysquid button, who presses Yellow King. Then they swap). If that's the case we may be stuck with Yellow King, since we have no control over when our regular Psysquid will show up in the temple, nor which button he will press. That's, of course, assuming every reality is just as important as every other, because if there was a higher-priority reality the Psysquid on that reality would be able to "force" changing with others Psysquids without them needing to press his button. Also with a higher-priority reality the Psysquid on that reality may be able to swap with everyone even if they're outside of the temple, meaning that Less-priority-reality-Psysquid could be on a mission when high-priority-reality-Psysquid activates his button, and they would swap mid-mission. That would make things very, very complicated to keep track of.
-That is all assuming two things: Each reality has access to every other reality (else, in OUR temple there could be four buttons, representing our four "neighboring" realities but there could be like 50 or so realities that we can't access from our own; and that the buttons refers to REALITIES and not to PSYSQUIDS, because if Yellow King Reality had Yellow King in it, after the swap Yellow King Reality would have Regular Psysquid in it, so it would become Regular Psysquid Reality and our reality would become Yellow King Reality, since Yellow King is now here and not there.
If we're assuming correctly, the what we need to have Our Psysquid back would be to have him, on the reality he is now, on the temple pressing his own button WHILE Yellow King is in our own reality's temple, pressing his own button. Then they would swap.