The reflex is automatic. The Fed signals a hike, and anything with the word mortgage in its name gets sold, because everyone knows higher rates kill origination volume. That reflex was correct when mortgage companies were loan factories whose earnings lived and died with the pipeline. It is much less correct now, because the balance sheets of the large non-bank mortgage companies are no longer dominated by loans held for sale. They are dominated by mortgage servicing rights.
A servicing right is the contractual claim to collect a small annual strip, typically around 25 to 30 basis points, on a loan's balance for as long as that loan stays alive. Its value is therefore a duration bet in reverse. If the borrower refinances, the strip disappears and the asset is worth nothing; if the borrower is frozen in place, the strip runs for years. This makes the MSR one of the very few negative duration assets in finance: it gains value when rates rise. Crucially, the large servicers carry these rights at fair value and remark them every quarter, so the gain is not a slow accrual that shows up eventually. It lands in the income statement in the quarter the rate move happens.