Missing/Old/Wrong Epics
Problem/Observation
You got Epics in Jira that have Stories and Sub-Tasks that people book time on. Now you've noticed that the Exply report shows more hours than Tempo does. This seems to happen when Stories are subsequently moved to another Epic.
Tempo reports reflect that shift. But in Exply, you still have Stories in the sum of all times per "Epic Name" that are already assigned to another Epic - even after a re-import of the Tempo data.
Solution
If you subsequently rename an epic, ONLY the issue name of the epic changes, but the separate "Epic Name" does not change automatically too (see screenshot below). This will sort the times in Exply according to the "old" Epic Name field and not according to the new Issue-Epic-Name.
You can therefore see if you did also adjust the "Epic Name" field to match the new Issue-Epic-Name. Then run the data-import again and it should then add up the times as expected.
Epic-Issue-Name vs. Epic Name field
Background
For a better understanding of this topic, here is what happens. In the Jira ecosystem, epics, stories, and tasks are basically all issues themselves, but with different issue types and relationships/hierarchy.
If you subsequently rename an epic, ONLY the issue name of the epic changes, but the separate "Epic Name" does not change automatically too (see screenshot above). This will sort the times in Exply according to the "old" Epic Name field and not according to the new Issue-Epic-Name.
If you choose the "Epic Name" field in Exply, it always uses the Epic Name field from the Jira issue.