How can a standard user backup everything using Time Machine? I have concern regarding this behavior.

When I use Time Machine as a standard user, it backs up everything (including data of users I do NOT even own). I realize that I still cannot access it, but how legit it is to allow me to backup everything on a system used by multiple users on an external hard drive and take it away with me?
You need to be an admin user to turn on Time Machine or change the disk - if you are an admin user you can see all the data on the machine.