Beacon does not take care of the server. You will have to manually start the server. Whether you do it after hitting start or before is entirely irrelevant though.
In addition you may use services such as
http://www.canyouseeme.org/ in case connecting to your external address does not work (which may occur on some cheaper routers).
More detailed information can also be found on the port forwarding wiki page (
https://www.spigotmc.org/wiki/port-forwarding/).