You'd be surprised. Lots of things and particularly cams beacon out to their P2P servers or otherwise try to make various outside connections regardless how you may have things selected under settings.
To restrict a device in the Asus routers, on the default main screen that comes up after you login (or click Network Map) click the circle above where it says Clients: (some number). That will bring up a list of connected devices in the right-hand pane. Find the device that you want (may need to hit refresh to update if it's newly added) and click on the image next to it. That will bring up a box where you can change the name of the device, change the associated image, then down below toggles to block Internet access, set a time schedule for access, and for MAC and IP address binding.
Also under WAN you can turn off UPnP at the router which will keep anything from setting up ports on its own. Under Administration make sure that "Enable Web Access from WAN" (aka remote administration) for the router is turned off, disable SSH and telnet unless you're using them, turn off IPv6 unless you're using it, and set various other things as you want them as far as logging, restricting IP access, etc.
If you want in the cams you also can blank or set to nonsense the values for gateway and DNS. That way they won't have any pathway out regardless what happens with the router/network settings. One catch will be (as will blocking Internet access) that they won't have access to an outside time server so you'd need to either provide an internal time server or sync to something else. Don't know how the NVR you have handles that. May be able to point it there. Also turn off all unwanted services within the cams like P2P, UPnP, etc., if you haven't.
As long as the NVR or VMS is pulling from the cameras and you're accessing them through it then the above shouldn't affect access remotely and you still can access the cams directly by IP when within your network. You will need to permit Internet access to a cam if you need to access it directly over VPN from the Internet for some reason. You can take it down temporarily by accessing the router via VPN and do what you need to do and then switch it back off.