It's unlikely on a Wilkie because of the saddle design, but there may be a sharp edge to it. Happens all the time on TOM-style saddles. More likely the nut has it. Either way, the string will bounce over and back a wrap (which can be good-sized on low E string) as you change tension/length. Usually you can hear it do that, though. Sounds like a "ping" as you adjust the string. Make sure the break angle over the nut isn't too severe. Contrary to popular belief, just because some angle is good, more is not better, and too much is just wrong. You may have to pop the string out of the slot and put some back angle on it so the string goes straight to the tuning peg with no bends over any corners.
