Thanks. Looks like the 6e RAW deals with this situation. I never noticed this in 5e and just assumed.
Page 26 has a sidebar on facing as well. There is no official facing rule, but they suggest it is a 0 phase action that cannot be taken at the end of a phase. I would simply rule otherwise in the situation you describe. If someone is already engaged in combat and their opponent moves around, I just assume they track the movement for "free" as part of the flow of combat. This of course introduces other problems, but I hunk if it's done with some constraint in situations which make sense, there's no problem with it.
Of course, once you take away the surprise bonus as the rule suggests, the point pretty much becomes moot.