I don't know anything about MCCC.
I've played games like this before though.
You probably know you have the choice to set aging to "active household only" if you want to only have them age while you're playing them. I find that's my favorite way to play rotationally- I feel like I don't miss out on their lives.
What do they get up to in the background?
Mostly, they only get up to whatever they can get up to when they're on the lot you're playing with the other sim. They might chat with other NPCs in the background, for example, so they might have new people in their relationship panel the next time you play them. They also might gain skill in areas they can practice while on lot-- for example, gaining dancing skill if they show up at a nightclub where you are playing with the other sim.
They do not earn money from their careers while unplayed. They also don't gain or lose career or school progress. With the important exception of university, but it sounds like you know that already.
If they are pregnant, the pregnancy will continue to progress while they're unplayed, so stick around for the birth if you want to be there :)
Check your Neighborhood Stories settings for "My Households" to make sure you have it set the way you want.
If you don't want the other sim to show up at all while you're playing the other one, you can use a mod that controls which sims appear in which worlds. The fact that you have them living in separate worlds is handy for this. Kuttoe's HomeRegions is the only mod I have installed and I love it.