In this case I'd go with the "all of it is true" mindset.
If time passed for the character, it did. If there was something that happened to their world, it did. If someone's character is now 'powerless' because of the dimensional shift, then it happened, and if this is the universe your character was always in and nothing has happened and still have all your powers... why not?
To me, at least, I could easily brush it aside as "Wow, something serious went down in some other dimensions. Glad it didn't happen to mine!" or "Wow, something crazy happened in other dimensions too?!" Some people referred to switching servers as 'dimensional hopping' (and as I had Lyc's on different servers, they had different powersets and slightly different backgrounds...)
Instead of being 'distracted' by it, why not try and incorporate it into roleplay?
Serious Swan is friends with Duck of Delights. They played together on the same server back in the day... they come here. SS wants to roleplay that the world ended, there was darkness, and now she appeared here, no idea why. DD wants to ignore that ever happened, so this is their world and nothing has changed. When they meet, they know each other, but quickly realize they aren't the same friends from the same dimension, even though they're exactly alike.
So many RP opportunities for discussing what they think happened to their respective friends from their dimensions, and where they may be... finding their friendship again, and if it's the same even though technically neither of them are different from the ones they knew. (maybe it'll give them opportunities to change little aspects of their character that they may have decided they didn't like, but didn't want to change at the time)
Putting together the pieces as to what happened to whom could be a big server-wide RP event in and of itself. I never did much of the Pocket D style of roleplay back in the day, but it sounds like a lot of collaborative storytelling... This could be another angle to explore.
*shrug* could be fun.
Lyc~