Actually, the cult team should process it instead.

Got you covered, badmins spawning cult on other modes.

code/game/gamemodes/cult/cult.dm

@@ -97,22 +97,6 @@
 				main_cult = C.cult_team
 	..()
 
-/datum/game_mode/cult/process()
-	if(finished)
-		return
-	var/datum/objective/sacrifice/sac_objective = locate() in main_cult.objectives
-	if(!sac_objective || sac_objective.check_completion())
-		return
-	var/datum/mind/sacrificial = sac_objective.get_target()
-	var/mob/living/t_current = sacrificial.current
-	if(!sacrificial || !sacrificial.current) //target is gone for good but not sacced.
-		main_cult.sort_sacrifice(TRUE)
-		return
-	if(QDELETED(sac_objective.target_current) || sac_objective.target_current != t_current) //target is now a different mob (monkey, simple mob)
-		sac_objective.sac_image = t_current.get_sac_image()
-		sac_objective.target_current = t_current
-		sac_objective.update_explanation_text()
-
 /datum/game_mode/proc/add_cultist(datum/mind/cult_mind, stun , equip = FALSE) //BASE
 	if (!istype(cult_mind))
 		return FALSE

code/modules/antagonists/cult/cult.dm

@@ -242,6 +242,30 @@
 	var/cult_risen = FALSE
 	var/cult_ascendent = FALSE
 
+/datum/team/cult/New()
+	. = ..()
+	START_PROCESSING(SSprocessing, src)
+
+/datum/team/cult/Destroy()
+	STOP_PROCESSING(SSprocessing, src)
+	return ..()
+
+/datum/team/cult/process()
+	if(SSticker.current_state == GAME_STATE_FINISHED)
+		return
+	var/datum/objective/sacrifice/sac_objective = locate() in objectives
+	if(!sac_objective || sac_objective.check_completion())
+		return
+	var/datum/mind/sacrificial = sac_objective.get_target()
+	var/mob/living/sac_current = sacrificial.current
+	if(!sacrificial || !sac_current) //target is gone for good but not sacrified.
+		sort_sacrifice(TRUE)
+		return
+	if(QDELETED(sac_objective.target_current) || sac_objective.target_current != sac_current) //target is now a different mob (monkey, simple mob)
+		sac_objective.sac_image = sac_current.get_sac_image()
+		sac_objective.target_current = sac_current
+		sac_objective.update_explanation_text()
+
 /datum/team/cult/proc/check_size()
 	if(cult_ascendent)
 		return

modular_citadel/code/game/machinery/cryopod.dm

@@ -246,13 +246,6 @@
 /obj/machinery/cryopod/proc/despawn_occupant()
 	var/mob/living/mob_occupant = occupant
 
-	if(istype(SSticker.mode, /datum/game_mode/cult))
-		var/datum/game_mode/cult/M = SSticker.mode
-		var/datum/team/cult/C = M.main_cult
-		var/datum/objective/sacrifice/S = locate() in C.objectives
-		if(S.target == mob_occupant.mind)
-			C.sort_sacrifice(TRUE)
-
 	//Update any existing objectives involving this mob.
 	for(var/datum/objective/O in GLOB.objectives)
 		// We don't want revs to get objectives that aren't for heads of staff. Letting