I'll just paraphrase and condense what I already said up front when I brought this up to begin with.
We have a palette of choices to choose from to decide what it is that actually happened, and some of these choices are mutually exclusive, with radically different implications for what had transpired. That's not a narrative. So many events in the film depend on Finn's defection, so it's not like this is a trivial or esoteric point.
As to what I'd propose, I already made one proposal that involved adding only a few more seconds to the film that would have cleared it right up, but having mulled it over I think I'd prefer something like the following.
Finn could have been getting escorted by a couple of troopers to reconditioning when he decides to turn. He has to kill them both which upsets him all the more; they were also his brothers in the corps. Fortunately no one notices. Everybody else thinks he's getting taken of, right? He hides the bodies. He's in a hurry to rescue Poe not just because he's worried about getting caught doing that, but because he's worried about the bodies being found and it getting reported that he never showed up for reconditioning. I don't believe there's any evidence that something like this didn't happen, and given everything that's been said arguably it's quite believable that something like it did. Phasma after all seems to believe he was going to get taken care of in reconditioning. Something happened to intervene. So, why not something like this?