Tempest Strike Flat Damage Scaling

I have a question about Tempest Strike. If I am focusing on a melee tempest strike beastmaster. I have a decent amount of flat melee damage scaling with the attunement node crashing waves, warcry talents and frenzy totem. But if I get flat cold/lightning/physical on my weapons does that flat damage only get applied to the corresponding strike? Is it worth it to get flat on my weapons or just go for crit/crit multi on weapons?

Flat is applied to hits. Adaptive/implicit melee damage from weapons will be converted to the type of the strike.
Added flat such as “27 melee physical damage” will be added to each strike, but will remain as physical damage. (Or whatever the damage type it states)