Your timer ticks down whenever you're expected to make any kind of move, whether that's actually taking your turn, or responding to a trade offer on another player's turn.
I'm not sure what you mean with 2 hours prior to my next review? Turns just run per the game, so can run faster than the indicated speed. So theoretically, in a 4p game with 4 turns/day, you'll only need to take one turn every 24 hours, since every player has 6 hours to take their turn. But if all three other players take their turn within 10 minutes of each other, it'll be your turn again pretty quickly. The other point is that in a game like Catan, sometimes players clocks will run concurrently because they're all expected to make a move (eg. responding to a trade offer). So from that POV, it's very unlikely to be 1 turn for you in 24h. You can either turn on notifications for when it's your turn, or make sure you're checking in regularly (for a 4 turns/day game, that can mean checking in multiple times each day).
The three Catan games you were recently booted on were two fast-speed turn-based (12 and 24 moves per day) and one real-time game. Those run with playing hours - a 12 hour period where your timer ticks and 12 hours where it doesn't. If those playing hours don't align with when you're on BGA, then you're likely going to run out of time easily.
Finally, the player in your currently running game with 4 days used a time joker two days ago (for whatever reason). This adds 4 days to their playtime for all games (used when you're unexpectedly away or something). That's the only reason they have so much more time than you. Generally, the maximum for a 4 turns/day game is 24 hours, everyone starts with this and it is only replenished by 6 hours each time it comes to your turn (for any reason, as I said above). If you are only coming online every 25-48 hours, then you're not going to be able to keep up with much beyond the two slowest turn-based speeds (1 turn/day and 1 turn/2 days).
All that said, I play almost exclusively 4 turns/day games, and I am usually on multiple times per day, during my waking time. The only times I get time penalties are in tournaments (which have a different timing mechanism) or when I have a particularly busy day and only check in maybe once or not at all (which only happens every so often, and is usually caught up using my time buffer, unless I get a really bad run of busy days).
