The notion that interest rate increases lead directly to home price declines is derived from the mis-application of a microeconomic concept (How much less house can I afford if interest rates go up) to a macroeconomic measure (Home prices).
Interest rate changes do not live in a bubble, they impact and are impacted by other factors in the economy. Higher interest rates typically accompany higher inflation. Higher inflation is the result of increases in the price of goods and services. This typically includes labor and housing.