the logical answer is yes, as logging out of facebook means you are terminating your active facebook session. so any connected sessions on the device like facebook login should be terminated.
This can certainly be a hassle. If this is in the context of being used in a personal device where there is only 1 user, or maybe 2. Then It'll fine to keep the user signed in.
But if this is a publically used device where many people login and log out like a computer in a airport or a cafe, then the above logic should be applied because users might not remember if they logged out of the websites they signed into