Word for "person that I supervise"
direct-report is often used.
I'm having a meeting on Tuesday for all my direct reports.
From Merriam-Webster, a supervisee is a person being supervised. The word has over 600,000 google hits, so it isn't really outdated.
What about 'subordinate'? Perhaps a tinge too militaristic, but it is very close in my mind.
Specific context is important because amongst my friends there are the following supervisor/supervised relationships:
Team Lead / Team Member
Office Manager / Staff Member
Manager / Direct Report
Unit Coordinator / Unit Staff Member