MX records may take up to 24 hours to propagate to ALL MX servers, but some may update faster than that. That's why you'll see some mail going to your old mail server, and some to your new mail server until all records have propagated fully.
The host names in{1,2}.smtp.messagingengine.com are still valid, but deprecated. The recommended values are in1-smtp.messagingengine.com and in2-smtp.messagingengine.com. See this blog post from 2012:
https://blog.fastmail.com/2012/01/06...s-for-domains/.
To see what MX records are reported for your domain by a handful of MX servers globally, try
http://mob.net/~ted/tools/mx.php3.