domain name system - Email not working correctly after DNS update

I have my domains at name.com where they are pointing to cloudflare DNS name servers.

After changing webhost I have changed my server IP address at CloudFlare.

My setup is this:

A localhost points to 127.0.0.1 Automatic       
A example.com   points to xxx.xxx.xxx.xxx   Automatic       
CNAME direct    is an alias of example.com  Automatic       
CNAME ftp   is an alias of example.com  Automatic       
CNAME mail  is an alias of example.com  Automatic       
CNAME www   is an alias of example.com  Automatic       

MX example.com  mail handled by example.com Automatic   

However - after 48 hours - I am receiving email on both my new and on my old webhost email (i.e. I have setup two email accounts in thunderbird - both info@example.com - that each check a pop3 at either the old or new webhost)