Time dilation does not "know" who is traveling faster. Instead, time dilation is a consequence of the fundamental principles of special relativity, which state that the laws of physics, including the constancy of the speed of light, are the same in all inertial reference frames.
In the context of time dilation, it's important to understand that the perception of time is relative to the observer's frame of reference. When two observers are in relative motion, they will measure different rates of time passing for each other.
Consider two observers: Observer A and Observer B. If they are in relative motion, Observer A may perceive Observer B's clock to be ticking more slowly, and Observer B may perceive Observer A's clock to be ticking more slowly. The perception of time dilation is symmetric, meaning each observer sees the other's clock as slower.
So, it is not a matter of one observer "knowing" that they are traveling faster than the other. Both observers are valid in their own frames of reference, and they each perceive time dilation relative to the other due to their relative motion.
The concept of time dilation is a consequence of the geometry of spacetime in special relativity, where the relative motion between observers leads to a difference in the elapsed time measured by each observer. It does not require any external knowledge or awareness of who is moving faster.