Here's what round splitting looks like in practice - All 3 of these coinjoins were created at the ~same time with a total of 626 inputs and confirmed in block 845572:
You can see the first tx has 65 BTC while the other two have 10 BTC, so the whales mostly managed to get into the same round as one another. This sorting is a result of the "MaxSuggestedAmount" being set lower in one round than another.
Theoretically, it would might be recommended to avoid them, but practically, there is no internal function within the client that would let me know they're running rounds in parallel, AFAIU. That's something I need to manually check. For example, I need to notice that my coins belong to different coinjoins. Isn't that correct?
Your wallet won't register inputs to two different rounds at once, it only registers inputs for the same round.