Keyword "previous" owner, not current owner. The previous owner is not known to YOU, therefore you do not have any obligation to the previous owner. The rightful owner is the person who offered you (and signed) the lease agreement.
A court of law will determine whether the "previous" owner has entitlement to rent payment. Trust that the legitimate owner will want to collect the rent and will do so in proper legal order.
Maintain multiple copies of the signed lease agreement and ALL cancelled check payments and receipts. Set aside an escrow account to maintain separate deposit of rent payments to show a court that you were/are willing to act in good faith to pay the rent due. The signed lease agreement, cancelled check payments and receipts, and the balance due for rent payments will justify your legal disposition.
Send a certified letter addressed to both the current and "previous" landlords requesting proof of ownership. Then file a small claims against both to get a court date to establish the truth. Sounds like a scam that may be the fault of the "previous" landlord.