Employers usually ask about investigations/LOI's separately.
Engaging with the FAA is not an administrative action as I see it. An admin action would be a formal action taken to address some issue, and would be documented in some manner. They would have to do an investigation first and then decide on an action. An investigation in and of itself is not a violation or administrative action.
If they determined that you had committed a violation and basically "diverted" your case to Compliance Action, I'm not sure if that would be admin action because Compliance Action specifically does NOT include a finding of violation.
But an employer might see it differently, so if you got Compliance Action I would probably consider that as an admin action just to be safe.
If you just talked to the FAA about some event, that conversation is probably not an admin action.
As far as having been investigated, that's a formal process. If you are investigated, you WILL get a letter in the mail (LOI). If you talk to the FAA but never got an LOI, you were not investigated (FOIA your records to be sure there's no LOI in your file).