Question : DNS records and mail

I have a customer of whom we recently transferred DNS,mail and web hosting over to Network Solutions.
They were on Megapath who also gave them a rudimentary form of web mail.

The problem was ,if we use anybody else's the new DNS records(Comcast,ATT) the webmail login comes up as Network Solutions,which is what it's supposed to do.
However,when using Megapath's DNS ,it gives their hosted web mail login page.
And to top it off,some emails were still going to their mail server on Megapath.
I called Megapath and they said we needed to notify them so they could change their DNS records.

I was under the impression that within a reasonable amount of time (24 to 48 hours)that ALL DNS records worldwide would reflect the change.

Is this just a lazy ISP or is am I wromg?

Answer : DNS records and mail

Before you made Network solutions the authoritative DNS for the zone, was that delegated to Megapath? If so, they don't automatically get updated that that has been changed. Once they are made aware of that and remove the authoritative zone from their DNS servers, they will get automatic updates from Network Solutions just like everyone else.