Can summon phantasm apply poison with poison support skill?

Hi is there a way to check it or anyone got any source or a solid point of this working?

I want to link them to my minions but all of them are melee and it seems that the only skill that give both the melee minion (that summons it) and the phantasm extra damage.

I already using minion speed and minion damage with them and empower that apparently makes the phantasm level higher too.

I'm just unsure if the spell hit also counts as "hit" for the poison support gem needs.

as long as minions hit and deal phys or chaos damage, they can poison and the poison support gems apply to them just fine

in PoE, hit is everything which is not Damage over Time

but in general poison support is not worth it for damage, because unlike players minions do not have access to DoT multi and other stuff that was introduced to compensate for "double dipping" fix..