A lease turns into a month-to-month rental agreement only if the tenant is not asked

I signed a 12 month lease stating that after it was completed I would automatically be in a month to month lease. 5 months after completing the 12 month month lease my landlord sent me a letter asking me if I wanted to sign another 12 month contract. I DID NOT sign a new contract, during this time my rent went up. At the beginning of the month I handed my notice in as my husband got a job in a new state. Almost 3 weeks after handing my notice in the landlord sends me a letter stating that because I paid the increase in rent that automatically bound me into a new contract and I have to pay rent up until the end of contract or until they can re rent. Is this legal.

[AFFA]

I wish to inform you that when your landlord informed you about the increase in rent those conditions will be studied in order to determine your liability. In this regard, if increase in rent was made applicable if new agreement was accepted then payment of increased rent will mean implied acceptance of agreement but if new rent was made applicable generally and no condition of accepting one year lease was made then payment of increase in rent amounts to payment on lease amount on a month to month lease as no new contract has been concluded.

AFF