Melee Martial damage, not any melee damage. (Some websites are out of date and do not reflect this change.)
You cannot use magicka skills to proc it. Magicka characters can use daggers (or other martial weapons) on the front bar to gain stacks with light attacks if they have no martial melee abilities.
I’m not sure Hurricane counts as melee, given its range, but ZOS has never been consistent about that across skills. Cloak has a smaller radius but ticks very slowly (once every 2 seconds), so even if it counts as melee it would take 20 seconds of constant uptime to reach max stacks and require careful maintenance.