...

Yes, Clockwork works with Tempo as well, but our plan for the future is to offer similar features that you won't be needing Tempo.

When time is logged into Jira?

Time spent on the issue is logged only once the timer is stopped. It means that currently Clockwork will log all time spent at the last day. It will not spread the time through days the timer was running.

How sub-tasks are handled?

When working on a sub-task time spent is reported only on the sub-task. Parent issue is not updated so you should not keep the sub-task and the parent issue in progress at the same time.