The first thing I think of when I hear about a Cat going full auto is the sear/trigger assemblies getting worn out. Could also be the bolt/hammer area where the sear catches getting worn out too.
If the sear and hammer look good, it could still be a worn area on the top of the trigger piece causing the full auto bursts.
Still, there is a slim chance it could be your recock and velocity settings helping cause that. Can't rule that out until you mess with those settings a little bit.
Not sure what your question was about the Alley Cat. I'm pretty sure the rear part of that bolt/hammer won't work with the Puma. I've read that it's a different size. I haven't owned an Alley/Thunder Cat to compare them myself however.
If you are using a siphon tank in the vertical position, it won't function normally. I think the tank needs to be tilted slightly so the tube can rotate to reach the liquid.
If you have the bottle mounted horizontally in front though, I don't know what to tell you other than to try another siphon tank.