No, it isn't automatic. Go to "Account&Membership" -> "Membership Details". There you can view your active entities and when they currently expire. You "can" extend them there, but you shouldn't.
Spending any coins on boosters for an enterprise, or the "leader" country of an empire, for any entities that are not your primary will also extend such entities on the same cost basis. 1 coin per 1 day. So, something like a "Super-Boost" for corps costs 10 coins for that enterprise but will also extend the enterprise for 10 days. After purchasing the booster, you can return to the "Membership Details" page and confirm.