The seat (Martin Baker Mk 12a) has an on board electronic sequencer.
Having seen the vid it would be safe to assume that the sequencer chose mode 1.
Mode 1 is designed for low-speed/low-altitude ejection conditions. The aim is to deploy the main parachute as soon as practicable after the seat has separated from the aircraft. A drogue deceleration phase is not required so the bridle releases are operated very quickly, thus ensuring that the deploying drogue and bridle assembly moves rapidly clear of the seat in readiness for the immediate main parachute deployment. Modes 2, 3, and 4 cater for high-speed ejections at low and medium altitudes. These ejection conditions require a delay before the parachute is deployed, to allow the velocity of the seat to reduce. The stabilizer drogue provides maximum deceleration while maintaining the seat in the optimum attitude for the occupant. The sequence timings of modes 2, 3, and 4 progressively extend the drogue phase with increasing speed and altitude so as to ensure that the parachute extractor is fired only when the seat velocity has reduced to a suitable level. The drogue bridle is jettisoned shortly after the parachute starts to deploy, both to avoid an entanglement and to allow the seat to fall clear of the occupant.
Mode 5 is the high-altitude ejection sequence, in which deployment of the main parachute is delayed until the drogue-stabilized seat falls through the 18,000-feet altitude boundary. This allows the occupant to be brought down to a safer atmospheric condition in the shortest possible time. Once the parachute deployment sequence is initiated, the seat performs in an identical manner to that of modes 2, 3, and 4.
Mode 1, low speed - low altitude. The drogue bridle is released, the parachute deployment rocket motor fires to deploy the personnel parachute, and the harness release system operates to free the occupant from the seat. The occupant is momentarily held in the seat bucket by the sticker straps.
During the ejection sequence, the parachute deployment rocket motor fires, extends the withdrawal line, and withdraws the parachute in its bag from the headbox of the seat. The parachute canopy emerges from the bag, periphery first, followed progressively by the remainder of the canopy and the drogue. The extractor rocket and bag clear the area. The drogue and crown bridle impart a force on the canopy, proportional to airspeed, to inhibit full canopy inflation until g-forces are reduced.
The "bit" that falls into the sea alongside the seat could be one of two things:
a) The seat drogue and bridle......or
b) The main parachute deployment rocket with associated webbing and bits attatched.
It is not unheard of for the pilot to fall onto the wreckage of the crashed a/c. Didnt an UAS stude land in the burning wreckage of a harrier a few years ago?
I hope I got the above info correct?