I create new page with lots of validation controls, such as RequiredValidation, RegexValidation and so on. I found out that when I create these validation controls, it seems like it render both client java-script and server validation for me automatically.
I want to know, do I understand correctly or not?
Yep. That is correct. The built-in controls do server side validation (for security) and client side validation (for performance and user experience) for you.
Tip: Don’t add these validations to the mark-up, but add them through the code behind, as shown in this blog post, since it keeps your code DRY.