Exos are said to have had their memories wiped the same number of times as the numbers on their names (Cayde-6, Banshee-44). It is also said in a Rasputin grimoire card that Andal Brask (friend to Cayde-6 and former vanguard hunter, deceased) believed that Cayde-6 was Rasputin. He claimed he looked at evidence and that was his conclusion. So what if Cayde-6 awoke Rasputin but Rasputin wiped his memory completely of it. Thats who you talk about when you say that Rasputin was activated by someone else. Also we can speculate that Cayde might have known he was Rasputin before even activating him that's why he did it but also willingly wiped his own memory. This would explain how Cayde got the codes to enter for the stealth drive originally and knew Rasputin had another code.