but all bets are off with the tremsetter. the flat-after-pullups, sharp-after-dives things was a very consistent finding after installing the tremsetter, but wasn't as consistent with just the regular springs...so I dont' think it was entirely a nut problem for me. But you should still check to make srue the screws holding down the neck are snug. From my experience, a walking nut won't cause tuning instability to be subtle -- whammy action will make it WAY out of tune!
One thing it might be due to is string slipping, even though I think rich says this is pretty uncommon on his tech page. I think that also results in the counterintuitive sharp-after-dives, flat-after-pullups effect, because when you dive, the string slips towards the top of the neck, resulting in increased tension after letting the bridge rise to neutral. And when you pull up, the strings get stretched towards the bridge, resulting in them being a little looser when you return to neutral...
that whole last paragraph could be completely wrong -- Rich would know...I'm no expert, but I'm thinking that SOMETHING might be wrong with the nut on my jem, so I'm going to swap it out.