Does free Sunday on-street parking in Belfast mean a private multistorey must also be free?

No.

DfI’s Sunday non-charging arrangements for paid on-street controlled-zone bays do not determine the tariffs in private multistorey car parks. Belfast has council, DfI and private parking facilities operating under different terms. A shopping centre may charge on Sunday even when the nearby charged street bay has no payment due. Read the signs at the exact entrance, including closing times, before leaving your car; free parking and access to retrieve a vehicle are separate issues.