Compression waves are easier to understand in a spring. If a region of the spring is compressed, that region presses outward on its neighbors harder than they push back. The region expands. If a compressed region is moving, the region ahead of it gets compressed and the region left behind gets stretched. These effects combine to make waves travel down the spring.
If you are looking at air as a bunch of particles bouncing around, it is easy to miss that air acts like a spring. In a region where there are more particles, they bounce into each other and the neighboring region. The neighbor doesn't have as many particles bouncing back. High density means high pressure. The denser region acts like a compressed spring and spreads out. A less dense, lower pressure, region gets pushed into. It is like a stretched spring and gets compressed.
So the same thing that makes a stretched pulse in a spring reflect off a wall makes a rarefaction region of air reflect.
Instead of a sine wave, imagine a single pulse of rarefaction approaching the wall. At the leading edge of the moving pulse, air from the normal region ahead of it flows in, leaving less air in the normal region. Inside the region, air moves toward the tail. At the tail, moving air piles up raising the density back to normal.
When the leading edge of the pulse hits the wall, there is no more air ahead of it. There is a low density region next to the wall. Air from behind pushes in and piles up against the wall. This high density region pushes itself away, leaving behind low density. But now the low density is following a normal density region moving away. The pulse has reflected.
This loose qualitative description just tells roughly what happens. It leaves a lot of questions unanswered. When a rarefaction pulse propagates, why does density return to normal? Why not higher or lower? For more details, you need the math.