webserver no longer sending email to outside sources like gmail or hotmail

We previously hosted our own email and have switched to a new hosted email system. When we were on our own email system our webserver was able to send mail without problem to wherever it needed. Since we switched we get the following in our mail log.

now we changed the smtp settings in php.ini and opened ports in the firewall to allow access to our hosted email server.

When I try to telnet to one of the ip's below on port 25 from the webserver, it times out.
When I try to telnet to one of the ip's below from my home on port 25 it connects.

I don't manage the servers, I manage the websites (which are no longer sending any type of email unless it is to one of our internal domains).

Is this more to do with the firewall? What needs to happen to allow these connections to go through? And why is the webserver trying to connect gmail/hotmail/yahoo etc if we have set up the smtp settings to use our hosted provider...

May 17 01:38:06 i007 postfix/error[3886]: CC0234C236: to=<xxx@gmail.com>, relay=none, delay=296083, delays=295933/150/0/0.01, dsn=4.4.1, status=deferred $
May 17 01:38:06 i007 postfix/smtp[3359]: connect to m.mx.mail.yahoo.com[66.94.238.147]:25: Connection timed out
May 17 01:38:06 i007 postfix/smtp[3366]: connect to mailin-03.mx.aol.com[64.12.90.33]:25: Connection timed out

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