There is a job in the scheduler creating the search indices. It’s just able to work if you execute your cron.php file regularly, but I can’t remember if it’s needed for basic or advanced searching (I assume it’s the advanced search).
I’ve checked the scheduler, seems that the jobs referring somehow to search are completed with no errors.
I think that only fields that change to this blue color are really indexed. Not the other ones (including custom fields “Complete Academic Title” & “Specialty”. See below:
Tbh I believe the blue color should just indicate that the field is clickable (in your screenshot from left to right: open the record, send a mail to the shown address, click2call).