the "pushing against" occurs when the rocket's explosive exhaust pushes against the tail of the rocket. the exhaust is the reaction mass. the matter that makes up the exhaust is the reaction mass. the exhaust is a gas and can not act as a compressor against the spacecraft. jumping off the earth is equivalent to you and your feet being the exhaust and the spot on the earth where your feet touches it being the nozzle on the spacecraft. you don't need to push against the air to push against the earth and the earth doesn't need to push against the air to push against you. it's inertia does that. in the nozzle example the gas released pushes against the nozzle. in the the ion thruster example the ions are pushing against the mass driver on the spacecraft. the force is not pushing against the external environment. it is the mass of the particles pushing against the mass driver. the mass driver does not rely on pressure. it relies on a powerful electromagnetic field pushing ions away from the mass of the craft. the fire hose example is even easier. perhaps you have heard the phrase pushing rope. the water coming out of the hose, once it leaves the hose no longer has any ability to push against the hose because it is liquid and can not act as a compression against the hose. it is in the act of leaving the hose that it pushes against the nozzle creating the reaction force.
RE: Do rockets work in Space?