Rude didn't leave over a contract dispute, he left because he was pissed about Montreal. He called Bischoff from the locker room that night looking for a job because after what he just saw go down with Bret, he wanted no part of the WWF anymore. Rude was old school and didn't like what happened one bit. The fact that he was only on a per-night deal is what allowed him to leave so quickly and show up on Nitro the following week. Mick Foley quit that night as well but was eventually talked into coming back.
JR is still a salty prick about it but I believe his beef stems from him claiming that he and Rude had a verbal or handshake agreement on a new long term contract then Montreal happened and Rude left for WCW, whether that's true or not, who knows. Rude did nothing wrong, it was just business.
Rude's appearance on both shows on the same night is definitely a memorable moment in the Monday night wars. It was another 'gotcha' type move from WCW who at the time was still kicking the shyt out of the WWF, sadly though, it was the only memorable thing Rude did during that whole run with WCW, IMO.