i have da same problemo
Every tournament game, well, I've played in only one so far but all games have that issue, not regular daily games so far. https://www.chess.com/tournament/just-for-fun-lt-1600
It's this one. Here is an example of it showing the red asterisk even though no variations have been saved.

I tried recording it https://www.dropbox.com/s/pxncrkyispchruk/2019-05-06%2023-26-10.mkv?dl=0
The next round in the tournament has started and it seems like all games are affected the same way, no variations are saved.
Unfortunately that's a huge time waster if you spend time calculating variations and then can't look them up after the other player made their move which can take up to 24 hours at which point you need to calculate everything from scratch, at least I don't remember all the variations I looked at after some hours.
In daily games you can play stuff out on the second board and save your variations. Usually you can try different whatifs and play moves for both and save it.
On certain games it's not saved even if you click on save. The save button is always orange as opposed to it being grey until you make a move when it does work.
The games where it doesn't work are from a tournament. Is saving of your own analysis not allowed in those for some reason? If it is, the save button should stay grey all the time.
Sometimes there is even the red asterisk thing on the second board that indicates that it has been edited, but no variations have been saved.