No, that doesn't mean that. They likely pay their property taxes through their mortgage via escrow. Since it all comes from the same payment, that means their mortgage payment rose, even if it wasn't tied to the actual mortgage.
Property value in most places absolutely sets your taxes, which is part of your monthly mortgage payment
So yes, the principal+interest doesn't change but when most people talk about their monthly mortgage they talk about the total amount they pay to live in their house that they're making payments on