The reflected image of the palm tree is accompanied by the reflected image of the sky above and surrounding it. so in the reflection, you see the palm tree and the sky. There is no pool of water: the light coming towards you from the palm tree and the sky behind it is reflected up away from the ground by a hot layer of air right next to the ground, which acts like a mirror and inverts the image of the palm tree.
Note that at a shallow angle close to sea level, the sea far from you also acts like a mirror, reflecting the blue of the sky, when the surface of the sea is calm and nearly flat. The reflections swirl around a bit because of small waves that "bend" the mirror surface around.
Because there are weak air currents next to the hot ground in the mirage case, the reflections from distant objects get swirled around in a manner that looks like the surface of a pond with small waves in its water.
These effects are easy to demonstrate if you put a table tennis table out in the sun and at one end, you install miniature palm trees. Somewhere near the middle of the table you place a large flat mirror and next to it a very shallow plate with a thin layer of water in it. Then go to the opposite end of the table, get down on your knees, and put your eye right next to the edge of the table and look towards the little palm trees, moving your head until the reflectors are in your line of sight.
With care you can do this experiment with a big flat plate of hot metal in place of the mirror but you might start the table on fire.