If you need any further guidance, check out the following information: Set up Office 365 - Office 365 for enterprises

In short,

- You need to first register your domain in Office 365, and go through the verification steps to prove that you own the domain. You can do this by placing a unique TXT Record/MX Record into your Public DNS.

- Once you have done this, you will then be provided with the MX Records, CNAME Records, TXT Records you need to place into your Public DNS to ensure mail-flow, autodiscover etc. works correctly.

- Then, You need to assign the relevant licenses to your user accounts, and ensure they have the correct SMTP Alias applied to their account.

You shouldn't have any issues, if you follow all of the steps.

if you are experiencing unexpected behaviour, post it up on here and I am sure someone can help you out, or log a support ticket via your administration portal.