Re: This sounds a bit odd.
The drogue parachute (the only part of the ejector seat relevant to this discussion) fires after the seat starts descending. Any earlier and the seat would just tangle with the drogue before it opened. The seat and occupant need the drogue to deploy to stablise both of them in a feet downwards position. Once stablised, and below a set height, the pilot is detached from the seat and sent on his (her) merry way. Then the main parachute opens and the remains of the pilot float gracefully to earth.
The initial cartridges which start the chair rising are powerful enough to get the seat clear of the airframe. Many twin boom aircraft had high level tail planes and these had to be cleared without the advantages of the rocket assisted ejection seats now used. The extra lift given by the rocket assist is to get the seat occupant up to parachute height, a must if the rest of the seat deployment / pilot separation / main parachute opening is to take place.