Emails Checker only determines if the recipient email address exists. It does not test the anti-spam policies employed by the receiving mail server, as no mail is actually sent.
Make sure that your mail server’s DNS data contains valid MX, PTR, and SPF records. You should also check that the sender’s address exists and that mail to this address is accepted by your server.
Additionally, your mail server needs to have a good reputation in order to send emails reliably. Cleaning your email lists before you start a new email marketing campaign helps a lot.