On Xbox -- Triple Shot is not working properly with Shotgun. Crit penalty from the doctrine is applying, but one shot is only hitting each enemy once (1 damage number). Triple Shot is working fine with other weapons, like the Boltgun and Heavy Bolter; they are triple shotting so I get 3 damage numbers per single shot.
On PC -- Triple Shot works fine with Shotgun. Crit penalty from the doctrine is applying, one shot can hit the same enemy 3x (3 separate damage numbers).
UPDATE -- After further testing, triple shot on xbox is: WORKING with burst shot, NOT WORKING with single shot. But burst shot is the main/only attack I'm using, so okay enough I guess.