bind configuration to external web server - help required

Our web server is now hosted externally, along with our domain name. We are
still using the same domain name space internally, along with the old web
server.

Internally my users are accessing the internal web server, while externally
users are accessing the external web server. I would like decomission the
internal web server but am trying to change the IP address for the web
server to the external IP address.

This does not work, and users are still accessing the internal server for
whatever reason.

Can someone please suggest how they are still accessing the internal server
when the A record now points to the external DNS. And how do I set it up so
users can access the external web?

Cheers,