Question about ee and trigger gems

Hi i'am planing on making build based around cast on melee kill. I wonder if i use lets say added fire (for don't know maybe ground slam) and add in fp and arc will they proc ee for each other or will they count as one hit (and then proc all 3 elements same time)?

they will not count as one hit, they'll occur in whichever order they hit (which should be the fire attack first, then probably arc then FP).