Remember that all attacks are declared before any are resolved, and that they are always made, even if the unit that declares them is destroyed before their turn comes to make them. Only after all attacks are made and all attacks resolved comes actual damage application.
So, it would be:
Everyone declares their weapon attacks for the turn
Everyone resolves their weapon attacks for the turn
Everyone applies the effects of damage resolution
The confusion comes from #2, where you actually have to see what damage is done as part of resolving a weapon attack, even if you don't actually apply that damage until afterwards. But if you remember that all declared attacks must be made, you know that those rounds of ammunition are gone, because otherwise you wouldn't be able to resolve the Blitzkrieg's attacks. As such, the critical hit to the Blitzkrieg would resolve onto an empty ammo bin, which still absorbs the crit but causes no explosion.
Essentially, mark off all ammo usage at the time you declare attacks. This is mentioned on p. 103 of TW, but buried a bit: it will be clearer in the final release of the BattleMech Manual.