"Sword and Storm," the traited Lightning component of Staff-Strike, doesn't seem to ever crit. There is no variance to its damage (that is, it deals a fixed quantity of damage as do, for example, the initial hit of the Burning Embers DoT, the Ring of Fire not-main-hit, the initial hit of the Sticky Gourd DoT, etc.), and its damage is dependent on your Tactical Damage Rating rather than your Staff Melee damage. It also does very little damage.
Ring of Fire's not-main-hit is completely independent of your Tactical Damage Rating; it is not counted as a DoT for the purpose of the Minor Class Legacy "+X% Fire Damage Over Time." It is, however, affected by your Tactical Mastery.
The Weapon Legacy "+48% Fire Skills Critical Damage" seems to be weird... non-Fire Crits seem to do 219% of the usual damage, but my Fire Crits seem to do 239% of the usual damage, specifically using the first hit of the Improved Burning Embers DoT (as it has no variance). 20% != 48%.
"Burst of Flame," the cash-out damage effect that Lightning Storm and Strike give by consuming a Burning Embers stack, is really really weak and has no variance in its damage. It also seems to be unaffected entirely by the Weapon Legacy "+48% Fire Skills Critical Damage," as when it critically hits, it deals 219% of its usual damage rather than 239%.