I guess it's time?

Mutter has an input thread. It currently can’t update the cursor position as directly as Xorg‘s input thread though, largely due to limitations of the current atomic KMS UAPI. Mutter‘s cursor movement is quite snappy anyway though, the difference in terms of input –> output latency is at most a few milliseconds.

AFAIK the situation is similar with other Wayland compositors.

None of this has anything to do with the Wayland or X protocol, how cursor movement is handled is purely between the display server and the kernel. (As a side note, Xorg‘s asynchronous mouse cursor movement was first introduced as „Silken Mouse“ in XFree86 4.0, when X was of similar age as Wayland is now)