I’m pretty sure that these traits are individual traits specific to the troop.
Meaning “Pyromania” and “Aflame” are specific to the troop dealing skull damage and not applied to the team globally when dealing skull damage.
If you want one of these traits to proc, the troop with the trait needs to be the one dealing the skull damage.
Also, on a side note… I’m pretty sure “Adjacent” dealt damage are unaffected by any multipliers.