No. The Fed sets rates for the Fed Funds rate and the discount rate, both of which are overnight rates for member banks who need emergency liquidity.

Mortgages are long-term debt. There is no relationship between long-term debt and overnight rates. In the United States, mortgages are benchmarked to the 10-year US Treasury note. Over time there may be some correlation between rising Fed rates and the 10-year Treasury, but it certainly isn’t a direct catalyst.

All Treasury prices reflect market dynamics and supply and demand. Fed rates are policy driven. The two will rarely move together in the short term, but if they do it would be coincidental.