I’ve tried this, on a plane, and on a train. I came down on the same spot I jumped from, both times.
I’m not sure about the physics involved, but that answered it for me! I think it may be because you and the plane are both moving forwards together at the same speed when you start. Your jumping just changes your vertical movement, but not your horizontal movement. It would take something like air resistance to slow your horizontal movement down, relative to the plane, to make you land on a different spot. You don’t get that air resistance inside the plane, because all the air in the plane is also moving forwards with you horizontally. So you come down on the same spot in the plane that you jumped up from.
Alternatively, try throwing a ball through towards the front of the plane. For the same reason, it still gets to the front of the plane, and doesn’t slow down in the air and start coming back towards you. But I think if you tried that in an “open top” plane like an old biplane, with the air rushing past you because you are moving forwards through it, the ball would slow down – or even get carried away in your slipstream.
Now if your plane was not moving forwards at a steady speed – for example if instead it was accelerating very hard like a jet fighter during take-off – and you did your jump, then I don’t think you would come down on exactly the same spot. Because in that case, although you and the plane are moving forwards together at the same speed when you start your jump, during the jump the plane’s forward speed changes if it is accelerating. But you are no longer connected to it during your jump, so you’d carry on at the same speed as when you started, and come down slightly behind the spot where you jumped from.