Firstly I believe that Onatel is the single most powerful mana controller in these types of events (other than the new heroes that have the same-but-improved specials).
Mindless attack-type specials are really good too because they will force mana back down to zero regardless of which mana tier the boss had reached.
Regarding your specific question I think you are correct that a mana gain prevented will not stop a boss that is beyond tier 1 from necessarily firing whereas a silence will. A mana cutter will stop the boss from firing if the mana cut brings it below tier 1 but otherwise same case as above. I am not competely how Hansel’s special will work however.