When the server has the Jetpack activated, Zombies will be turned off. If the server has the Jetpack deactivated and 'monsteremitter' custom blocks exist in the world, Zombies will spawn, and other players will not be able to activate the Jetpack. Players will only be able to activate Jetpack again when the server host activates their Jetpack. If there are no 'monsteremitter' custom blocks in the world, there are no restrictions to Jetpack use for players.
The Jetpack relic was brought into the game with its initial release on April 8th, 2011. It was brought into the game as one of the 9 original relics.
As of Content Patch 10, the Jetpack can be toggled on and off with the 'Back' button.