Thats how it worked at Mesa. If I recall first priority were Mesa pilots, second priority were pilots in that system (I may be wrong but I think both the Mainline partners and other X Express were at the same priority), and then anyone else.
@USMCmech just finished IOE I think (?) so he might know if its the same or has changed.
Incidentally, I found it usually less complicated to fly on non-partner airlines. Like, I was in the United Express system and I think at the time United (or maybe Mesa) was toying with the concept that if you asked for the jumpseat and ended up with a seat in the back you should pay the $20 or whatever segment fee as if you were using pass travel benefits. My absolute favorite was AirTran out of ATL or Frontier out of Denver. Their flight attendants and pilots were always so nice to commuting pilots. The Frontier flight attendants usually swiped me free TV, and I usually got my favorite seat in the back of the 717 on AirTran -- the sound of the engines always put me to sleep!
My least favorite on the DEN-SAT leg atleast was SWA, but only because they were usually pretty full. I had to sit in the
second jumpseat on the 737 multiple times. Always fun when the captain reaches back for that tablet computer trip can thing they used and you meep: 'Sorry that was acually my balls, sir'.