Earth rotates from west to east, but not every planet in the Solar System rotates in the same direction. For example, Venus, the "morning star," rotates from east to west.
Expanding this to the universe, there are even more planets that do not rotate from west to east. Uranus's rotation is even stranger. In short, if one merely recorded Earth orbiting the Sun and played it backward, it would not look particularly strange, because this conforms to Newton's second law and the law of universal gravitation. This is called time-reversal symmetry.
However, many laws in the macroscopic world do not satisfy time-reversal symmetry. For example, a river flowing from high ground to low ground would look very strange if "played backward" and made to flow in reverse.
When the Time-Turner was turned, the scenes of the day rewound instead of one simply "traveling" directly to a certain point in time and then having time continue flowing forward.
Just as a broken teacup had to move along the same path to return to its original starting point, one could not directly return to several hours earlier. One had to walk backward along the river of time for several hours, and throughout that process, everything one saw was played in reverse.
Hermione turned the Time-Turner in the ward. Assuming Harry had remained in the ward the entire time, he would have seen his rewinding self "grow younger," while the version of himself within the Time-Turner's chain continued aging. Yet Ron Weasley, who was also in the ward, saw Hermione and Harry vanish together, then reenter through the door from outside the Hospital Wing.
First of all, Harry and Hermione's "spatial coordinates had not changed." When they reached the appointed time and pushed the door open from inside the Hospital Wing, it was