How and When Can You Collect Month-to-Month vs Lease Rent Amount?

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Hi all, this is my first post. My question, what is the procedure to collect a new increased rent amount from tenants? And what would you do in this situation? I have a rental property whose lease expired in August. That lease stipulated a higher month-to-month rate if no new lease were signed. On the advice of my property manager I increased the month-to-month rate and the leased rental rate for the new lease. It's been THREE months since the old lease expired. The tenants have neither signed the new lease nor increased their rental checks. The property manager has been operating under the assumption the tenants WILL sign the new lease. I have been asking my property manager repeatedly why he is not collecting an increased/correct higher rent amount. Finally he told me this week he would "send them a notice" that they were now on month-to-month terms and need to pay the higher amount. I am very confused. I thought rentals automatically turned into month-to-month after the lease expires. Also, aren't I owed back rent at this point? Details: Rental is in DC