If the User ID is very different from the User Name, so the stemming algorithm doesn't link them, then a task that references to the user table through that ID will not be found by a search for User ID.
The search engine does not go over the referenced tables from records found in the search results. Only if the searched text pattern is found in both tables User and Task/Incident, like a user full name, then the results will be presented from both tables.

 

1 - Login any instance as admin.
2 - Open the OOB user record 'Asset Manager' and notice the User ID 'itam'.
3 - Give this user the itil role and a group, so to be able to assign incidents.
4 - Modify a few existing incidents setting the Caller to 'Asset Manager'.
5 - Modify a few existing incidents setting the Assigned To to 'Asset Manager'.
6 - Wait for the indexing to refresh on the newly modified task records.
7 - Perform a global text search for 'Asset Manager'. Notice the User record is found, and all the modified Incidents are found as well.
8 - Perform a global text search for 'itam'. Notice the User record is found, but none of the modified Incidents are found.

This is expected behaviour. Only the display values for the referenced user, i.e. 'Asset Manager', are indexed and retrievable by the search.