Exhaust leaks are pretty easy to hear, and they don't sound cool. I would assume you don't have a leak, but if you are not into cars much and wouldn't notice the sound of a leakey exhaust, maybe go out start the car and double check for unwanted sounds coming from the pipes. Even a small leak at the header connections is very noticeable. Its possible the new system is just breathing better than the old one.
More likely, it is the mixture. counter intuitive, rich doesn't backfire. Lean backfires at about 2000 rpm coasting with the tranny in 4th. It is more apparent as the deacceleration increases, like coasting down a hill. When mine is lean, it doesn't like to rev in 1st. Half way through a light, at maybe 3k, it stops pulling, I need to shift to 2nd. If it is too lean, you are going to be surprised how much power you are loosing. There are 3 approches to troubleshooting it: 1) An easy check is to loosen the altimeter add another washer of about a 1/16in. I would wrench the devise loose, then warm the motor so the WRD is not sucking air. Then unscrew the altimeter and listen to the rpms to change. I'll guess they should go up as you back it out about a few turns. turn the motor off, add the washer/shim and test drive the car. Don't leave it too loose, it will keep backing out till the car won't run. That should bring the mixture rich enough to diminish the backfire if not eliminate it. Keep adding shims until it sounds and feels very good. Get back to us with the results.