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If you want to know more about the way we calculate time please check out Version 1: algorithm for calculating How time spent is calculated (assuming with working hours are the same for all days)?

Is it compatible with Tempo?

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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.

How to see Organizations on the timesheet?

See Break down time by Organizations from Jira Service Management