do these benefit from melee damage or just the base hit? I know it says they are spells but I just wanted to make sure
Neither, the spells are their own separate procs that benefit from the usual spell-y things (increased spell damage, adaptive spell damage, relevant element damage, spell crit, etc). If the tooltip for the spell says it has a base damage then that would be added to any adaptive spell damage you have, but not the melee damage that you have.
As a side node, all spell triggered by Tempest Strike do gain dmg from attributes associated with Tempest Strike(in this case attuenment and strength)
I think the descriptions urgently need to be improved. In addition, there is no proper overview of damage components / skill. I think that should be revised for all skills.
It desperately needs a node to convert Melee damage to spell damage and Cast Speed to Melee attack speed