Every new exhaust leaves the workshop with something on it. There is drawing lubricant in the seams of the tube, cutting fluid around a weld, a protective film on polished surfaces, oil from handling, and often a sticker or a plug somebody forgot to remove. None of it is part of the part, and all of it has to leave.
The smell is those residues cooking off. It is strongest early in the first proper drive and fades as the surfaces clean themselves. The useful tell is that it declines. A smell that holds steady or grows is a different problem, and knowing which of the two you have is what stops an owner from worrying about a system that is behaving normally.
Some finishes and some gasket materials are designed to change when they first get hot. A coating that cures gives off a sharper smell than oil and usually arrives at a consistent point in the warm-up, then stops. That is the material working as intended, with nothing to correct.
The distinction from a contaminant is repeatability. A curing coating smells once and is finished. Assembly residue smells for a while and then tapers. A plastic bag left resting on a stainless muffler smells briefly and then leaves a visible mark, which is the point where you stop diagnosing a smell and start looking for melted material.
Not every smell under a car belongs to the exhaust. Underseal softening on a hot floor, a cable tie giving up, a rubber boot near a pipe and spilled fluid on a hot casting all produce odours that owners attribute to the new part. The giveaway is location: an exhaust smell follows the tailpipe, and everything else is strongest at the front or the middle.
Another way to separate them is to note when the smell appears. A system burning off announces itself as the pipe warms and fades once it is at working heat. A melting component arrives later, stays while the car is hot, and returns every time without any taper. That pattern means something is touching that should not be.
An exhaust leak does not usually smell like burning. It smells like exhaust, which is sharper and more acrid, and it often arrives with a noise or a soot stain. The case that matters is a leak ahead of the cabin, because that is the one putting gas where people sit rather than trailing it behind the car.
Treat a suspected front leak as a stop-and-check item rather than something to monitor. Look for a soot trail at the flanges and along the welds, listen for a tick that follows engine speed, and if the smell is inside the car with the windows closed, do not keep driving it. Find it before the next trip.
The residues leave faster with airflow and varying load than with idling, because idling heats the pipe slowly and lets the smell sit in one place. A normal drive does the job without putting anything under stress. Parking and revving in a garage does the opposite, concentrating the smell where nothing is moving air.
What to avoid is putting anything cold onto a hot system to clean it, and fitting a cover or a wrap before the surfaces have finished smoking, since both trap the residue against the metal. Add an exhaust heat shield after the burn-off rather than before, and the smell will not be baked into the shield as well as into the pipe.
Stop and inspect when the smell comes with visible smoke that keeps coming, when it is stronger inside the cabin than outside, when it changes into something sharp and chemical, or when it has not clearly reduced after several proper drives. Any single one of those is enough to justify putting the car up and looking.
If none of that is true, the correct action is to drive normally and let the surfaces finish. A pipe that smells for a few days and then stops has done exactly what it should. Recording the smell on video is more useful than describing it later, because a smell is the one symptom you cannot reproduce for anyone after the fact.