OK, my bad. Now I understand that part of the question. I don't know where IB gets the shares. Perhaps it's a just a book entry? Perhaps they are lending you shares overnight at no borrow cost as a service because they will get the shares by the morning from the counter party? I dunno. But does it really matter? The shares are in your account immediately - upon call exercise - to do with as you want and how they got there is semantics and perhaps a future "Trivial Pursuit" answer. as well. The real issue here is the details of the trade (stock price, strike, premium, dividend (if any ??) and why that led you to believe that this was a good trade to execute.
Yeah, it's just a shown on paper. You technically become the owner of the shares from the counter party upon exercise. Brokers assume this as a cost of doing business--because if we could facilitate these trades directly with the counter party, there'd be no reason for brokers. It's their raison d'etre.