I think it's brilliant to say that the Halkans sent Kirk's landing party into a virtual world, a simulation of some kind, as a test of character.
But what about the mirror universe characters arriving on “our” Enterprise? Is that an illusion Talosian-style, then?
My old explanation was that the mirror universe never existed until this particular ion storm interacted with the Enterprise transporter. As Kirk's party beamed up, the whole other universe sprang into existence at once-- an inaccurate, fuzzy carbon copy of the real thing. [If time travel can generate whole alternate timelines instantly, how big a stretch is this?] When the episode concludes, the evil four disappear because their whole universe disappears.
I hope you don’t mind that I disagree. IMHO, that’s such a big stretch that I find myself unable to estimate the end of it. This whole concept of alternate realities popping instantly into existence from practically nowhere would require some kind of intelligent design by somebody like a Q (maybe the peace loving Halkans did have a Q as their guardian angel?).
I also find it somewhat problematic that the pacifist Halkans, who are afraid their dilithium could be abused to harm somebody else, would have no problems on the other hand to put Kirk and company to a character test with a high probability they could get harmed or killed. For a Q that could be a completely different issue…
On the other hand, what exactly did Spock do aboard the Enterprise all that time before stating “I assume they returned to their Enterprise at the same time you appeared here”?
Kirk used the computer as a means to figure out a way to return them to their universe, it stands to reason that Spock did the same on “our” Enterprise.
I think there is a high probability that he calculated the amount of time it might take the others to rig the transporter, had the mirror characters brought, tranquilized or whatever in the transport chamber and waited for the transporter beam impulse from the mirror universe that would tell him that our characters were arriving so he could send the mirror characters to the location the transporter beam was coming from.
I think the fact, that Spock and Lt. Kyle were in the transporter room the minute that Kirk and company arrived back from the mirror universe tells us exactly that.
Obviously Spock was expecting their return on the transport chamber’s platform, otherwise there would have been no reason for him being there.
Bob