I work with a fair number of exotics. I primarily do costume collars. I have that edge problem as well. Here's a few things that seem to help:
1. Make sure to rough up *at least* the surface of whatever leather the scaled leather is going on. If its uber thin like snake, it's going to be difficult to impractical to rough up the exotic... however, when working with something a little thicker like carp, I'll go over the exotic with a l50-220 sand paper.
2. I use regular screaming death- yellow issue Barge cement too for my "first attempt at adherence". I try to remember to apply the skin on one edge then "roll it down" the rest of the surface- I'm fussy enough to trim off the excess with nail scissors or a cuticle cutter (looks like a really tiny light duty edger... good for lots of exotics I've used except stingray or shark.) I like to press it down with a heavy roller to avoid little air pockets.
3. If the edges still pop up and there's enough room to peel the layers back where they don't stick, I'll actually re-apply the barge as a contact cement. If there isn't even enough room to get a little brush with the thick goo in there, I like to use something more flexible... believe it or not, hide glue or even (DUN DUN DUN!)... Aileen's Tacky Glue. Then I clamp with heavy duty clothes pins with or without pads. Most of my projects end up flexing a lot while in use- if this was not the case, I'd use Gorilla's Super Glue.
4. When my shapes aren't sharply curved or highly irregular, I will cut the exotic in the right shape but purposely leave the edge a bit long- like a 1/2 inch or more on 6-8 oz leather. I glue everything down with barge, and muster the restraint to leave it alone overnight. Next day (or whenever I get back to the project) I get a nice soft paintbrush and wet the underside of the stick-out edge a little. I pull that over the entirety of the backing leather edge as tightly as it will go without separating the scales. After pressing all that into a smooth edge, I clip it all down with safety pins (usually with pads) and let that dry... with NO glue. Once it is dry, I'll gently peel that edge away enough to apply glue... since you sew your exotics on, you could leave enough of a "lip* *to sew through both the top and bottom edges. Sewn thusly- the edge is highly unlikely to pop up... ever.