In full, the question indirectly addresses the nature of conditional triggered abilities. Are they triggered and resolved immediately, or are there some triggers "pending resolution"?
Recently you ruled that "The Corp can use multiple Awakening Centers per run..."
I assumed this means that the encountered ice is considered to be "protecting the server". But other people tell me I'm wrong.
So, when the Runner passes all of the ice protecting a server, two Awakening Centers trigger, then one of the triggers resolves. After the runner passes that new ice:
1. The 2nd AwC's ability, that was trigged before and was previously "floating in the air" or "on the stack", resolves (that would imply that conditional abilities do nor trigger and resolve immediately - that is, there are triggers "pending resolution")
2. The 2nd AwC's ability trigger anew and resolves immediately (that would imply that the "when the Runner passes all of the ice protecting this server" condition is satisfied again --> the encountered ice was indeed protecting the server, so it would've benefitted from Experiential Data).
To my understandind the encounter with new ice should cancel any triggers left, since the runner is now someplace else on the timing structure of a run. Just like bypassing prevents its "pay 3 credits" ability.