It's a tricky answer to be sure, but the way the episode is shot and presented gives us more clues than anything. The episode opens on Ensign Wildman going into labor. She goes to sickbay, and Paris suggests heading through a plasma drift to avoid the Vidiians. At that point, Voyager is split in two, though we don't know this yet. What we see is that the baby is delivered, medical complications develop, the Doctor and Kes start intervening. At that point, the antimatter starts draining, the ship is hit with proton bursts, people start getting hurt, Kim dies, Kes disappears, and we don't know there's another Voyager until a good way through the episode.
At that point, we see the happy, "healthy" Voyager, but because it's so far into the episode, we've come to associate the "unhealthy" Voyager as the "real" one. Considering that it's the one that survives in the end, we can say that it is the "real" Voyager with reasonable certainty, or at least, that's what the creators of the show would like us to believe. It would make sense then, that the antimatter would naturally want to return to its place of origin, which is to say that it would go back to the "unhealthy" ship, which we've been following for the whole episode.
Given that this scenario has never happened on record before or after, coming up with an in-universe explanation is tricky at best. The best explanation I could come up with for this based on known information about antimatter and a thorough reading of the script is this:
The antimatter was attempting to balance itself between both ships. This caused the drain which affected both ships, causing both ships to attempt the proton burst procedure (though the duplicate pulled the trigger first). Once the duplicate stopped the proton burst, the antimatter started to balance, and upon destruction of the duplicate, the antimatter flowed to the first ship.
The "healthy" ship being the duplicate is substantiated further by the Memory Alpha entries (generally regarded as reliable sources for canon information) for Harry Kim and Naomi Wildman, who are both listed as dying in 2372 and being replaced by a "duplicate".
So in other words, the "unhealthy" Voyager was in phase all along, the antimatter was draining because of the actions of the "healthy" ship, and once that duplicate ship was taken out of the equation, yes, the antimatter did in fact "pop" back into the right spot (if you can call not moving "popping"). We know this primarily from the cinematography of the episode, and to a lesser extent, from the limited knowledge we have of antimatter and subspace scissions.