It doesn't sound like the rent increase needed to be "proposed", it sounds like you already agreed to it in the lease. It is in place.
Therefore your payments have been short.
You can make an argument that you relied in good faith on the paperwork they provided showing you were current on payments, which would likely secure you time to pay without invoking penalties, and the landlord can go after the management company for whatever reasonable costs he incurred from the delays. You shouldn't have to pay any penalties here. But I doubt you will get out of paying the rent you agreed to.