How fire tag on minions works?

If a minion skills have the fire tag (summon skeletons) do increase fire damage affix increase their damage?

Minion fire damage affixes will, yes. Player fire damage affixes won’t.

As @Llama8 said, it has to specify minion to affect them. If the affix simply says “increased fire damage” or something similar, that’s player-specific and doesn’t affect your minions.