If a Musi paid Hissa Jaidad on a house, do the heirs (if Musis) still have to pay Hissa Jaidad after inheriting it?

Yes. Upon the Musi's demise, the shares inherited by the surviving spouse and children become their respective properties. Hissa Jaidad accordingly becomes payable on the share inherited by each Musi at their prescribed Wasiyyat rate.

For example, if the surviving spouse inherits 1/8 of the house, they will be required to pay Hissa Jaidad on 1/8 of the assessed market value at their applicable Wasiyyat rate.