In the Star Trek, Deep Space Nine, episode "Crossover" two members of the DS9 crew crossover to an alternate universe. It is the same universe that Kirk went to many years earlier in the TOS Episode: "Mirror, Mirror."
In this episode the two members crossover going through the wormhole with some engine issues. This causes them to crossover.
In "Mirror, Mirror" Kirk crosses over due to an issue with the transporter.
Aside from the method of crossing over, there is one other major difference in the process, which is that the Kirk from the mirror universe crosses over to the prime universe at the same time as our Kirk goes to the mirror universe. In order for each Kirk to get back to his right universe, they had to recreate the same transporter issue in both universes at the same time.
However in DS9: "Crossover" the two crew members never exchange places.
Why didn't the mirror universe Major Kira and Doctor Bashir crossover at the same time?