NSEU
"Autostart" is not the same as "Auto-relight" - different logic paths in the FADEC. If the engine flames out or runs down uncommanded, it goes into Auto-relight. In Auto-relight it will obviously turn on ignition and adjust fuel flow for the burner conditions, and if there is evidence of a surge/stall take appropriate action to attempt to clear the surge/stall as well. If the FADEC sees the fuel switch transition it will enter Autostart which will then schedule fuel, ignition, etc. for an in-flight start (potentially with starter assist if the start valve is enabled). While the details vary between engine types (the 747-400/RB211 was a very early autostart implementation - the newer systems are much more sophisticated and complex), there is a major difference between auto-relight and autostart:
Autostart can turn off fuel and will respect EGT limits - auto-relight won't (although the inflight start EGT limit is higher than on-ground, autostart will still turn off fuel to prevent exceeding it).
BTW, the RB211/747-400 isn't really a FADEC - it's an FAFC - "Full Authority Fuel Control". It doesn't control the vanes and bleeds like a true FADEC - the vanes and bleeds are controlled by a fluidic (pneumatic) system that is little changed from what was on the early RB211s.