Warren Instigator's ability triggers when it deals any kind of damage to an opponent, not just combat damage.

If Warren Instigator attacks an opponent and isn't blocked, its double strike ability will cause it to deal combat damage to that opponent twice, once during each combat damage step. Its triggered ability will thus trigger twice: Warren Instigator deals first-strike combat damage, its ability triggers and resolves, it deals regular combat damage, and its ability triggers and resolves again.