It's every minute, and i assume they do it at intervals irrespective of how many seconds you've been in the fief, so i doubt it'll remove one troop exactly 60 seconds after your arrival, there'll likely be some preset time it applies it and if you're unlucky you'll arrive just as that happens.
That's what I assumed as well. But I assumed it would be on the "minute" tick when everything happens in strategus (i.e. people move into a fief at the same time, so I figured 1 full minute later it woul do the crime check, not 15 seconds later). My only guess is that since my guy doesn't actually move out of the fief until the next "Minute" tick, I got hit with the crime check. There should be a 1 minute buffer before it kicks in (at minimum, maybe more like other people are saying).
Either way, it's a pretty retarded mechanic if I'm in a fief for less than 15 seconds and I'm losing any troops. I did everything the "logical" way. I moved my guy 0.0 meters from the fief (without entering it) ,then when I was at my computer I hit "enter 'fief'". Hit F5 to refresh my web page every second (or maybe even more) until my person showed as entered the fief (looking at the weapon tab to see when it changed to all -2 quality horses), entered the total # of goods I had, hit "sell/confirm/whatever" and clicked on a new point on the map to move to.
The point of crime killing troops is to prevent people from stacking fiefs with troops or armies that can't be touched by other people. A 5 or 10 minute buffer to let people trade would be a good thing.