To connect to a Server you will always need Internet Access. You would need to be Sharing your File. To connect when your are off the Server's Network you will need to setup Port Forwarding and connect using your Public IP Address. If you have only one license of FileMaker Pro, you may need an additional license or the use of FileMaker Go on iOS to work as you'd like.
Also, I am going to move this thread from the FileMaker Community Feedback Space, which is specifically for input on the Community itself, to the Discussions Space where you should receive more views and potentially more advice!