Did you get a chance to go through Neo4j Server Configuration documentation? It says:
#allow any client to connect
org.neo4j.server.webserver.address=0.0.0.0
This line in conf/neo4j-server.properties
is commented by default and limits access to port 7474
to localhost or 127.0.0.1
(which probably is the reason why things work for your domain using that server and accessing Neo4j over localhost). Uncomment that line and it should make port 7474 accessible to everyone i.e. 0.0.0.0
.
In order to secure your Neo4j server with an Authorization layer, you might want to refer Securing access to the Neo4j Server documentation.