Mortgage rates will change more quickly than housing prices. Mortgage rates are a function of the Fed, Treasury Rates and tons of banks/lenders across the nation. National scale influenced, sure, in part by national demand for mortgages.

You local housing prices are more of a function of local supply/demand which is partially disconnected from the national scene. So yes, national mortgage rates going high will knock out some potential buyers. At the same time (at least in my area)... rates have gone up... local inventory of available homes has gone down (people just choosing to not sell) and thus housing prices are remaining mostly flat even as national mortgage rates rise.