In this video one can clearly see the difference between an ejection that only uses power cartridges (as in the older ejection seats) and a "new generation" seat that uses booster rockets as well. Notice how the seat separates from the dummy before impact with the rocket assissted ejection. The seat will typically stay attached to the pilot above 10 000ft to provide oxygen, and then automatically detach and fall away when the pilot descends below that altitude.
The seat in the Mirage F1 that inadvertently ejected Maj Aurhur Piercy at AFB Rundu in the 80's (read "Vlamgat" by Gen Dick Lord), did not have rockets to assist the ejection, as was normal for that generation of ejection seats. Those ejection seats required a specific forward speed (typically 60 knots), as well as a minimum altitude for a safe ejection.
The Astra, Hawk Mk120 and Gripen aircraft all are equipped with rocket assisted Martin Baker Mk10 ejection seats, for which you don't need any forward speed or altitude ("Zero-Zero" ejection seats).
