Restriction of a module sheaf to a closed subvariety ($\tilde{M}{|}_{\mathrm{Spec}(A/I)}=\widetilde{M/IM}$)

The restriction meant here is the pullback of a sheaf of modules to the closed subvariety, including tensoring with its structure sheaf. On an affine chart, tensoring $M$ with $A/I$ gives $M/IM$. This distinction matters because restricting only the underlying topological sheaf would retain the ambient ring action.