I ask not about the meanings "turn" or "turn around" which both verbs share, but only about the meaning of "leap" that appears new to Vulgar Latin and (superficially) unconnected to the notion of to "turn, roll."
This r/latin post assists.
rocketman0739. 1 month ago
It mentions that volutus meant “bowed, arched.” Leaping does create an arched trajectory.
CaiusMaximusRetardus. 1 month ago
I'm not sure I understand your question, but on what basis is volvitare founded ? The construction of the word doesn't make much sense and it doesn't seem to be attested. The -itare suffix usually denotes an intensive or iterative form, for volvere, it should be volutare.
Volutare means "to turn a lot/often", so I can see why it could mean "to leap" in some specific cases. Think of smoke, for instance, when you blow through it (it turns on itself and goes in all directions), or a rock rolling down a rocky slope.