I think that for the Servant Out of Time, you do not trigger the froced response wich is "After Servant Out of Time enter play" because he do not enter play. I know it's tricky but it should be play like that.
but I'm sure you do not trigger the forced response for the Deep-One rising wich is : "After you play" because you dont' play a Depp-One rising but a DoppelGanger.