As you say, the causality loop is so tight that if you remove any one element it all fall apart. So if someone other than Sinclair went back with B4 then his DNA probably shouldn't have set off the triluminary...then again having said that, I think Lennier did mention other pilots being taken in and "scanned" with a similarly positive result. But then, the way it's portrayed in ITB, that part appears to have been retconned.
Even so, it's almost certain the glow wasn't the giveaway that Sinclair had a Minbari soul. Heck, it can't even have been the giveaway that it was Valen's, because if it was, Delenn would've figured out her ancestry about twenty minutes earlier in "Atonement" when she remembered that the triluminary glowed for her and wouldn't have had to figure out what Dukhat's last words were.
I digress. My point is that triluminary is apparently quite the useful little gadget, even if all we've seen them do is knock people out, make the chrysalis machine turn on, and glow for people in the Sinclair family. The Minbari wouldn't have pointed their most sacred relic at some human nobody unless they expected it to help them find out where to bomb Earth first. So it probably has a more sophisticated way of determining and displaying if someone has a "Minbari soul" than just glowing, so it's possible that Sinclair might've always gotten a positive, even if someone else was Valen.
Or the alternate Babylon 4 timeline could've been wildly different, aside from the things I listed that we saw. I know the intent was that the timelines be the same up to War Without End, at which point either the crew steals Babylon 4 or there's a giant shadow attack, but it just doesn't parse.