I recently got a real world 777 mechanics rating and used the PMDG 777 to learn at home. I came across the same issue with the backup generators (referred to as BUGs). Also at my P3D PMDG 777 the BUGs show green on the synoptics page when the IDGs are switched off. But they don't supply power as they should. After I landed the BUGs also worked fine on ground.
Conclusion: The BUGs only work as supposed after the aircraft has been set to flight mode. Once the aircraft was in flight, the BUGs also work ok on ground. That seems to me like a fault in the PMDG 777 because I don't see any reason why the BUGs should work different in air than on ground.
I have access to real world, up to date Boeing documentation including AMM, SDS and training docs. According to these documents the BUGs supply their onside AC transfer bus if the IDG is not delivering power (switched off, disconnected, faulty, etc.). If both IDGs don't supply power the right BUG supplies both AC transfer buses. The BUGs deliver their power to the backup generator converter in the main equipment center. This converter is necessary as the BUGs don't include a transmission that keeps the frequency constant with varying engine speeds. The main generators are called IDGs because they have an internal gearbox that regulate the varying input speed to a constant 115V AC / 400Hz output. The BUGs can't do this (they're much smaller because of the missing transmission). As there is only one BUG converter installed on the 777 only one BUG can deliver power at a time. They can not be paralleled within the BUG converter. That's why the right BUG supplies power to both AC transfer buses if power is lost on both sides. If the right BUG is faulty the left one can replace it to power both AC transfer buses. But only one BUG can be active at a time.
If only one engine is running of course one IDG can supply both AC transfer buses (APU and external power off). The BUG needs a running engine just like the normal IDG. So if the engine doesn't turn the installed IDG and BUG are not delivering power.
Nowhere Boeing mentions that the system behavior differs between air and ground mode. And as I said the P3D PMDG 777 system behavior on ground changes after the aircraft has been set to air. This can't be normal.
After engine start the BUGs are checked automatically. You can see this also on the PMDG 777 if you monitor the ELEC synoptics page. The BUGs come online green for 15sec after ENG start. So after every engine start the aircraft checks its BUGs by itself. Quite cool.
The function that the right BUG (or the left one if the right one failed) supplies power to both AC transfer buses on the PMDG 777 only works when the IFE and cabin supplies have been switched off. I couldn't find any info about this on the Boeing docs. But maybe PMDG knows even more than mechanics do. Nobody knows everything about an airplane like this. If the IFE and cabin supplies are switched on the BUGs only supply their onside bus on the PMDG 777.
As I said I just made my rating. I'm not saying that I know everything. But this is how I understood it. If something is wrong or you have further questions I can try to find out. Maybe PMDG staff can look into this as well.