If you want to make it so that players ignite AND die at the same time (as in achievement_idle_inferno), Make a trigger_multiple with the ignite output, and then make a smaller trigger_hurt inside that trigger_multi. Make sure the multi's boundaries extend at least 20 units from the trigger_hurt's boundaries, or the player won't ignite.
Play around in hammer yourself with a little test map and find what works for whatever it is you're doing