Use modmii to update your softmod. An official update may remove some cIOSs and older versions of the hbc, nothing that can't be rehacked anyway but still, ultimately you'll want to block updates using priiloader
Likely those games are just missing an IOS that needs to be installed, 4.3U is the latest AFAIK, so the on disc updates will just update minor things that aren't included in the online update such as installing game specific IOSes.
The games in all likelihood could play now, remember he's on 4.3. The games may want to install a stub ios to various slots used for homebrew and that is triggering the update prompt. A Syscheck would confirm all that but in the time he does that he could just resoftmod using ModMii