One name for a thruster is a reaction motor. Put very simply, a reaction motor pushes mass in one direction at high speed. The motor (and whatever it’s bolted to) moves in the opposite direction because of the counteracting reaction. The thruster, doesn’t have to push against anything. The thrust accelerates the rocket as described by Newton's second law of motion. (SECOND LAW - The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object).
You get this effect when you fire a gun, such as a cannon. When you fire a cannon, it recoils—it moves backward. This is the offsetting reaction to the cannonball flying out the muzzle. Before you fired the cannon, nothing was moving. After you fire the cannon, the moving cannonball and the moving cannon cancel each other out.
Air has nothing to do with this. It’s all a question of balancing momentum. THIS was also a