can you ping the ip address of the DVR from outside across the VPN. The IP address you would ping is the same IP address you use to successfully connect when you are at home. For example if the IP address at home is 192.168.1.20 then try to ping that address from the outside world across the VPN. You can simulate being in the outside world by disconnecting your smart phone from your WiFi and just using the cellular provider network, if you want to use a laptop instead you could use your smart phone (again disconnected from your home WiFi) as a WiFi hot spot and access the Internet with the laptop.
This is likely an issue with the configuration of the VPN and the way it passes traffic thru to the private network.
It could also be a misconfiguration on the DVR, make sure the "Default Gateway", "Gateway" or "Router" IP address is set correctly on the DVR. You can check your home computer to see what the "Default Gateway" is set to and make sure it is the same on the DVR network configuration.
Make sure your firewall is not prohibiting the DVR IP address from outbound communications at least over the VPN if not the overall firewall.
Give us more information and we might be able to narrow your search for the problem. What make and model is the DVR, the Firewall, what is the IP info (IP address, subnet mask, gateway) on the Firewall (private and public) and on the DVR? What VPN client are you using on the remote device? what is the remote device (laptop, smart phone, carrier pigeon, shamanistic incantations...)