I'd have to go focus on it, but overall I think he has pretty good pocket awareness--especially the other night, when compared side-by-side with Haener. If he looks slow to climb it could be adjusting to the speed or maybe the Saints use different protections (for sure a larger variety) than he was used to in college.
Different types of protection create different windows and lanes for QBs. The most basic example would be *quick game vs. drop back* protection (I talked about it in another AMA - Derrick Carr not buying time with his legs on the strip/sack at the end of the Rams game b/c it was quick game pro). But it goes beyond that--identifying he defensive front and/or pressure, along with where the OL is sliding, where the back is inserting, is the TE chipping (because that changes rush angles), etc.
Brees was pretty much the king of working the pocket. If it were a recordable stat, he would probably be the best ever. We always think of it as him having this amorphous 6th sense--which to some extent, he did (great peripheral vision, etc.). But it was also b/c Brees was really, really, really good at identifying the front and pressure of the opposing defense. Back then the Saints used pretty simple protections up front and RARELY maxed up or got creative. You can do this when you have a QB who more or less communicates to his OL before every snap exactly what the defense is doing. He now knows who is blocking who, where the throwing windows are and where he can step and slide and climb.
All that to say--I'm not too worried about Rattler's pocket presence yet. He may not be Drew Brees, but he's got the instincts and is a natural. If there is something in his game that needs to be improved, he's got the ingredients to do it.