Disable internal e-mails?

Probably not the best title but here's my situation.

I am currently using the mail GoogleApp thing. Where you can setup your domain to point mail to your GoogleApp account. I added some dns entries on my domain(hosted externally @ godaddy) and all is good. I can send e-mails to person@mydomain.com.

My Problem:
I can't seem to send email to my domain from my VPS. For example using php Mail() doesn't work. When I do exim -bt -d person@mydomain.com I can see that it thinks the person has a email account locally because the vps has the same domain name as the email account. It throws lots of "No Such User Here".

Does this make any sense? If so..basically I don't want mail that has the same domain name as my vps to think that it belongs to user on the server. Is there any way to do this?