User-/date-aware script fields appear in the wrong panel after cache reset

To reproduce:

• Set up a scripted field that returns a user (or date) value, and configure its template and searcher correspondingly.
• Navigate to an issue where the field is visible and verify that it appears in the People (or Dates) panel.
• Go to Built-In Scripts > Clear classloader or jira internal caches, select 'Jira internal caches', and run.
• Reload the issue view.

Expected: The field stays in the correct panel.

Actual: The field now appears in the main panel and remains there even across reloads. It can be sent back to the correct panel by visiting the Script Fields page (no need to do anything there, just visit).

Other potential triggers of this problem (albeit with the same underlying mechanism) include saving the configuration of a Web Resource.