Also would an explosion in the exhaust not drive the turbo backwards?
Correct, bang bang antilag is adding intentional combustion in the exhaust manifold, before the turbo.
I would not have thought the small amount of unburnt fuel in the exhaust stream could be ignited but then again this is not my area.
These designs intentionally add more fuel and/or drop the spark to leave it completely unburnt and ready to go.
https://youtu.be/rmf0LveXwVkhttps://youtu.be/YvgaBWNjrFAWhen a rally car is coming, all you hear is "BANG,clatter, clatter ,BANG" and it still half a mile away.
Every time the throttle is lifted, instead of "Dump valving" the over pressure on the turbo, they do the opposite, they inject unburnt fuel into the exhaust and ignite it to detonate and keep pushing high pressure exhaust through the turbo. This allows they to run HUGE turbos with HUGE lag, but as the anti-lag fires constantly the moment they take the foot off the throttle, it's still spinning at full speed on the corner exit ready to apply full power.
On the start line, they hold it on a launch rev point. The anti-lag is running nearly constantly not quite full BANG, but a constnat machine gun of them.
The purpose of the 3-5 seconds like this is to spin the turbo up to full RPM before they leave the line with FULL boost instantly.
EDIT: It should be noted that this practice came under a lot of scrutiny. Ford used a large cylinder in the exhaust system and added valves to it. Then they charged the cylinder up with exhaust and used it to run the turbo. It was promptly banned.
However modern rally cars don't BANG and rattle. They chirp and crackle. Im not sure how they tamed it, possibly by making the detonation much more controlled and engineered rather than something worked out in a shed by a farmer once upon a time.