You drill holes on the back of the panel but
without going through the wood. Then you wind the threaded parts into the wood using the hex key. This leaves you with a flush top panel with no bolt heads showing and then you can screw the joystick onto the threaded mounts from underneath. When using those threaded mounts the joystick plate always sits against the underneath of the panel... not on the top like you have in your picture.
Undermounting or top mounting is personal choice. Top mounting makes the joystick handle stick up further by the thickness of your wood. Undermounting may make the handle sit too low for your liking.
Your work there looks very neat actually.

You can still recess the plate underneath but make sure you have enough thickness of wood to wind in the threaded mounts. You will need to fill in recess you have already made with wood putty or simnilar and then sand down. Or alternatively start the panel again with fresh wood.