Being triggered in a certain way does not change what type of skill something is. Nothing becomes a Brand skill due to being triggered this way, so modifiers which specifically apply to Brand Skills will apply to the Arcanist Brand itself (if applicable), but not to non-brand skills it triggers.
However modifiers specifically to Damge, Critical Strike Chance and Critical Strike Multiplier of Brand Skills, have all been changed to instead affect "Brand Damage" or "Brand Critical Strikes", which are new keywords defined as Damage/Critical Strike Chance of Brand Skills or any skills triggered by Brands. There will be reminder text on sources of those stats explaining that definition.
So for the damage and crit chance/multipler stats specifically, those have been changed to something which can apply to spells triggered by Arcanist Brand. Any other modifiers which still refer to Brand Skills will continue to only affect Brand Skills.