There's two problems, one is that if you wait to remove the RemJet till after, you end up contaminating the emulsion with more RemJet as it falls off the back between chemistry cycles, and two you contaminate those chemistries with bits of RemJet and then that carries over to the next round of development and it gets even worse with more contamination.

So removing it first is the better move I would think.

I don't know why it would cause any darkening of the film though, I've asked before and to my recollection PE said sodium bicarbonate shouldn't be causing any development issues, I can't recall why I was asking though, but I remember asking if the sodium bicarbonate could ruin the film and was told that it wouldn't.