How does a subsonic jet engine intake design ensure correct air intake?
Subsonic speed makes the inlet self-regulating. Add blunt edges, and the inlet works for a wide variety of engine and flight speeds, as it should.

An inlet is always a compromise. Therefore, it is quite a bit larger than what is needed in cruise in order to keep losses at low speed low. At low flight speed and full throttle the engine needs much more air than what is flowing into the inlet without the engine actively sucking air in. The flow lines converge from a much larger capture area when closing in on the inlet face and the stagnation point lies on the outer edge of the inlet lip.

Watch what happens when an airliner engine spools up on a rainy day, with puddles on the ground. When the engine reaches full speed, it starts to suck up even the water in the puddles below the intake! Some streamlines even come from behind, wrap around the inlet lip and get sucked in. With water droplets in them, they are very visible indeed.

At high speed, the capture area is much smaller than the inlet face. Only the central streamline stays straight, all others diverge away from that central streamline and now the stagnation point is on the inner edge of the inlet lip. Streamlines bordering the capture area flow around the lip and along the outside of the nacelle. This divergence of the streamlines is caused by the pressure increase ahead of the inlet, when the air is slowed down and exchanges kinetic for static energy. This even happens without friction losses, so the most efficient compression of an inlet happens ahead of it (in subsonic flow - supersonic speed removes that luxury).

The air speed at the compressor face is fairly constant at the same throttle setting, regardless of flight speed. Therefore, the pressure at the compressor face is lower than ambient at low flight speed (because air had to be accelerated) and higher at high flight speed.