I've found the link below which provides useful info on how to configure Time Capsule for remote connection. I've followed this and am able to connect to remotely manage the TC (via Airport utility) but still cannot connect in order to access files. I'm trying from a Windows PC.
The first thing to check is if the Time Capsule was told explicitly to share the files over the internet using bonjour or simply sharing to the WAN.
Have you verified that the active profile on the Airport is set to allow this?
My example has these turned off (you can see them under the guest access control)
Make sure that you have a clear path to the Internet in terms of firewalls, and ensure that TCP port 5354 and UDP ports 4500 and 5353 are open and unrestricted.
Once you've done that, make sure you are logged into iCloud on your computer, and that the remote Time Capsule is on (also making sure those ports are unblocked on that end). Your disk should now be available via FTP and AFP.
If you have access to a Mac, try these steps from the Apple Support Article about troubleshooting Back to My Mac.
- Update all your Macs to OS X Lion v10.7.3 or later (OS X Lion v10.7.4 or later is recommended).
- Choose System Preferences from the Apple () menu. Open iCloud System Preferences and check that Back to My Mac is enabled. See if any diagnostic messages are provided under the Back to My Mac section to assist you with troubleshooting and resolving any connection issue.
- Toggle Back To My Mac off and back on by deselecting and then reselecting Back To My Mac in iCloud System Preferences.
- Make sure the computer you are trying to connect to is not sleeping and is set to Wake on Demand. For more information about Wake on Demand, see this article.
- If you are using an AirPort base station, make sure your firmware is up-to-date (open AirPort Utility 6.0 or later).
- Check your network for a multiple NAT setup and reconfigure your network as needed.
- Make sure NAT-PMP or UPnP is enabled (if you are using an AirPort Extreme Gigabit Ethernet base station, click here for information about AirPort Extreme Gigabit Ethernet and NAT PMP).
- Ensure TCP port 5354 and UDP ports 4500 and 5353 are open on your firewall. To learn more about ports used by Apple products, click here.
Note: Perform these steps only if you've verified the information in the previously listed troubleshooting section is configured correctly.
- Open Keychain Access located in /Applications/Utilities.
- Choose the System Keychain in the Keychains list on the left.
- Sort the Keychain list by Kind.
- Select all keys listing the "Back to My Mac Key."
- Delete the selected keys. You will be prompted for your machine's administrator password.
- Quit Keychain Access.
- Choose System Preferences from the Apple () menu. Open iCloud System Preferences.
- Toggle Back to My Mac off and back on again by deselecting (if still selected) and selecting the checkbox.
- Once Back to My Mac connects, quit System Preferences.