No idea what you are saying. Sounds exactly like that - scaling combined with an animated box wipe to "crop". Anyway, it's a moot point. from your post it's 100% clear that you are a total AE beginner, so perhaps reading the help files might be a good idea. this is really basic stuff.
I agree with Mylenium. You need some basic training. After Effects is very complex, and without a good, basic knowledge it's just a matter of time before you get hopelessly lost.
...I saw this part of his video that shrink.
For example; the video size is 1080x720 and then it shrink to 720x720 without cropping or changing the composition scale.
This is why you need basic training. The video you describe is wide and not very tall, but it changes into something that is square. Two different shapes. It can NOT be done without cropping the sides.
Do yourself a favor. Go here:
Do you have a link to what you're talking about?
Definitely a confusing question since logically, you can't reduce the resolution and scale without actually reducing the resolution and scale. It also went to a square.
If I were guessing, it sounds like one of two things, you squeezed the sides in or letterboxed from the side kinda.
In any case, something was either lost or distorted to go from 1080x720 to 720x720.
Did you ever find a solution for your transition? Let us know what you did or if you still need help.