Sorry, didn't realize it was access. I believe parens will solve:
SELECT tblActions.intActionID, tblActions.intIncidentID, tblActions.intAction, tblActions.intEmployeeID, tblActions.intSupervisorID, tblActions.datActionDate, E1.txtEmployee
as EmployeeName, E2.txtEmployee as SupervisorName
FROM (tblActions INNER JOIN tblEmployee E1 ON tblActions.intEmployeeID = E1.intEmployeeID )
INNER JOIN tblEmployee E2 ON tblActions.intSupervisorID = E2.intEmployeeID