An experimentation on time dilation [duplicate]

In the video https://www.youtube.com/watch?v=ev9zrt__lec from 03:00 to 05:00

I hope that both the clocks would read the same equal amount ,say,1 revolution, in measuring the time elapsed for the flash to return to the laser fired.

And the both Sarah and Adam may feel the time elapsed to be different in their own perspectives which might have arised from "the speed of light is same for all observers.

I think i am right upto this extent.

Now, Is time dilation an illusive phenomenon in which one may feel "a one single tick of a clock" which can be "one minute" for another one WHILE for both of them, the clock is universal and runs at same pace ???

Why do Sarah and Adam feel the time elapsed to be different ?? in what way ?