In the situation above, ownership doesn't change hands until the contract is completed (i..e. the deed of transfer signed, and generally the purchase money paid over in full - commonly called "closing"). At that point title changes hands.
It can happen that a vendor will allow the purchaser in to the property before the contract is completed on a caretaker basis, but it would need to be stipulated in the contract, and in that situation, title still doesn't change until the contract is completed.