Usually exhaust popping is actually from lack or lesser of back pressure when the throttle is closed. Performance exhaust normally are more free flowing and promote less back pressure for more/top end power. As well, engine exhaust gases actually pulse into the whole exhaust (called exhaust resonance). So when going full throttle, exhaust gases are flowing/pulsing really fast and when there's a change in throttle, the exhaust flow and pulse is dramatically reduced. When this happens, the slow pulses collide with the fast pulses in the latter part of the exhaust causing a popping sound. Same concept as going full throttle in a boat with waves way behind you and suddenly pull the throttle to stop and the waves behind you catch up and collide with the boat. This is common with change to the exhaust system or muffler. As well, more acoustic or sound absorption helps reduce some of the popping.
On the other hand, the reason for popping (backfires) in the exhaust, there can be a host of reasons and they all do indeed have to do with fuel.
One reason is all engines have camshaft overlap (intake and exhaust valve are both open) which promotes fuel scavenging where it helps the engine pull air and fuel quicker through the engine while revving, but with the expense of some fuel going into the exhaust. The scavenging helps to engine to accelerate, but when a change in throttle, the scavenging is compromised and fuel gets burnt in the exhaust.
Another reason is when an engine is high up in the rpms and there's a close/change of the throttle, some engines pull out/retard the timing (10-20 degrees) while still at that high rpm. This results to a very late combustion chamber burn even by the time the exhaust valve opens, resulting a pop/backfire in exhaust.
Third reason would be a fuel enrichment. When a engine is a constant throttle, air/fuel ratio is about 14.7:1 whereas under acceleration usually it's more fuel, 12.5:1 for example. So sometimes when a throttle is closed, the carburetor or ECU doesn't change it back to 14.7:1 quick enough and rich fuel is burnt either in the engine or in the exhaust systems.
There are so many more reasons, like rev limiters, anti-lag setups, not enough sound absorption, and so on. But I hope I was able to shine some more light.
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