I’ve seen a few of these threads but no solutions. Car is a 94 LHD bone stock except for a racing beat dual exhaust. Brand new engine from Mazda. Almost everything under the hood is brand new. Stock pre cat and main cat.

Im in so cal so weather is about 60-70f. When I first start the car with a cold engine it stays at about 1500 rpm’s. The problem is it’s not a smooth 1500 rpm’s. I get vibration, minor shaking and popping. As soon as I hit operating temp the rpm’s drop to normal range and the idle is almost smooth. Not 100% perfect but feels nice.

I notice when I turn on the ac at operating temp, the idle is rougher as well. Just more vibration. Also getting noticeable pops out of the exhaust when letting off the throttle. I’ve heard the popping is normal with downpipes etc, but my car has the pre cat and main cat so not sure how loud normal is.

Any ideas?