If you do not have a Schengen or transit visa, then you can not go beyond the clearly established borders (in this case it is the territory of an international airport). However, since Malta entered the Schengen area, the visa on hand will be "the same", which will allow you to walk around Rome without problems, if docking implies a long wait at the airport.

In fact, docking involves a flight with a landing at several points, and throughout the entire flight, no matter how many transplants, there is one air ticket. Most often, the docking procedure takes about 2-6 hours, but there are also 24-hour waiting periods. When docking, it is necessary to pass safety control.

At the airport of departure, you register and receive a document that you present at the intermediate terminal. That is, you do not have to re-register in Rome. Border and customs control of tourists in the transit zone is not threatened.