In the timing report, there is a Clock Domains Analysis (CDC) section. It doesn't report if the CDC is handled properly through synchronizers or FIFOs.
This should be the designer's responsibility, as we currently do not have a DRC that checks for this. However, the CDC section will show if a clock has any cross clock crossing paths to other clock domains.
From here, user can manually check the concerned paths on the RTL and do the necessary update if needed.