"There is an HSA deduction on the dependents W-2 for himself only, not family."

This is not worded quite correctly, by the way.

The policy Coverage would be self or family. The HSA account is always personally owned. For example, you can have Family Coverage, and each adult (taxpayer and spouse) can have their own HSA account. There is no such thing as Family HSA. There is a $ Family limit, or a $ single limit, though.

Qualifying to have an HSA account or not, depends on the policy being high-deductible and meeting the IRS requirements. How much to contribution up to a limit, depends on the policy type, as single-coverage or family coverage.

If you qualify for half-year, you allowable HSA contribution also is half.