How can I constrain an imported netlist in Vivado?
One solution is to write an XDC file including the required constraints and attach it to the entity name of the imported netlist using the XDC file property SCOPED_TO_REF. (Attaching it to a specific instance with SCOPED_TO_CELLS should also work.)

When using the SCOPED_TO_REF property, it must be set to the original (top-level) entity named stored within the netlist. Attaching it to the entity name of the black-box does not work (*). Moreover, the XDC file must be marked as to use "only for implementation", otherwise the synthesis step complains a critical warning. The setting "only for implementation" already includes the post-synthesis timing analysis.

(*) When attaching it to the entity name of the black-box the synthesis step will be satisfied. But, it cannot attach the timing constraints to the netlist anyway.