For the FAQ (unofficial):
In regards to when the Corporation rezes an ICE with an "On encounter" effect: Similar to Inside Job, Backstitching would bypass that ice before the "On encounter" happens (but all "On rez" effects still trigger) due to the nuance of run timings. It is the runners turn so they get priority in paid ability windows.
Examples:
Funhouse would not apply a tag.
Anvil is bypassed before it's on encounter ability window.
Anansi would still deal damage.
Wave would still allow the Corp to search an ICE and reveal it.