I had the same issue. I could easily access locally but not over the internet. I fixed it after studying up on this networking stuff. I'm definitely new with this.
I found it was definitely like everyone says; port forwarding.
So my setup is my iMac/PC and Linkstation are connected to my NETGEAR ROUTER then to my VERIZON MODEM.
When connected to the ROUTER i could see the LINKSTATION locally but not over the internet.
When connected to the MODEM i could see the LINKSTATION over the internet but NOT locally.
I connected back to the ROUTER and had to forward the IP ADDRESS of the ROUTER via the MODEM.
So I logged into the MODEM, forwarded the appropriate ports/ip address and it worked!
So it definitely makes a difference when connected to the router or the modem. I knew this, but I didn't know how to fix it at first.