A bizzare problem when share files among a domain

BlankSystem environment:
2 computers, one is the server(domain controller), the other is
node_1. The domain name is test.edu. Node_1 is added to the domain
already.

I tried to share a directory on computer node_1, so any domain user
has full control.

For the permission button, the default group is "everyone",
first I remove it, then click the add button. The bizzare
thing happened.

1) for most of the cases, the location is node_1, which is not good, what
I want to is test.edu.
2) for some rare cases, the location is test.edu, then I can add
"domain users".

What I really want is case 2), how to solve this problem?

For security reason, it is pretty important for us.

Thanks a lot.