Is Dio's The World actually allowing him to move at the speed of light?
There's going to be some amount of magical hand waving in any time manipulation ability and I haven't seen Jojo or "the world" but perhaps it could be similar to a time stop from Artemis Fowl. A time stop is a finite zone in which time is stopped for the consciousness of all conscious beings inside. To those inside the only effect is that all communications and time dependent devices (clocks, TV, Phone signal, etc.) are stopped and living beings cannot fall asleep. Any natural processes happen normally, there's no wind but you can breathe but you cannot physically leave because the outside world doesn't exist in relation to a time stopped zone. When the time stop ends those affected by it instantly have their time set to normal time (e.g. if time is stopped at noon for 4 hours you experience noon for 4 hours and when it ends your time resumes normally from 4 pm). To those outside the field nothing appears wrong with the time stopped area and you can walk into it but any conscious beings who were inside are gone, trapped in past at the moment the time stop started and will only reappear when it ends. The time stop apparently only traps your consciousness in that moment and detains the body of anyone affected until it ends, this is why I guess the whole molecules/photons not moving isn't a problem.