I am quite familiar with the US-16E seat (as found on F-35) and quite a few others from the past such as the Mk 7A (found in the UK variant of the F-4).
As with all ejection seats, it is primarily an electro-mechanical system that is completely independent of the aircraft in the control sense. Obviously it is physically attached (or at least the mountings are).
In the more general sense, as with all modern ejection seats, it is a seat attached to a very powerful gun with a rocket pack underneath the seat pan.
This particular seat has an electronic sequencer that is used to determine the optimum crew / seat separation timing, the most critical of which is a 0 0 ejection. This is where the aircraft has zero altitude and 0 speed.
The sequencer is a completely closed system electronically so no remote attacks are possible and employs redundancy in the measurement and decision logic to reduce the potential for failure to extremely low levels.
The power for the electronics is provided by thermal batteries that are ignited when the seat starts to move.
The entire sequence of ejection is actually quite interesting.
Pull handle (there is only one nowadays). This fires the primary cartridge in the seat gun and also ignites the shaped charge in the canopy which blows out a large egress area.
Seat starts to move and power is applied to the sequencer which has a 'sensing window' to determine altitude and speed. Optimal separation time is computed. As soon as the seat starts to move, the drogue gun is fired. This fires a large metal bullet upwards which is attached to a drogue - a small parachute designed to stabilise the seat during descent.
The drogue won't deploy until the cord attached reaches it's limit which will not happen until the seat is well clear of the aircraft.
There are large spikes on each side of the seat above the crewmember's head which will clear any remnants of the canopy that may not have been destroyed by the shaped charge as the seat rises up through the hole in the canopy.
When the bottom of the seat reaches the cockpit sill, the under seat rocket pack fires.
At separation, the seat will cut the seat straps and tip the crew member out by firing EEDs (electro-explosive devices) to release the drogue, pulling the ripcord of the crew member parachute as that happens.
The parachute release mechanism also has a water automatic release system that will automatically release the parachute from the crew member within two seconds of landing in the sea. This is so if the crew member is unconscious, the parachute will not drown the person as it sinks.
There are some other details, but that is the fundamentals of operation.