I see it as BGs 3rd Gen started with EXO/BTOB in 2012, and GGs started with Red Velvet and Mamamoo in 2014. 2013 was like an empty year because there weren't that many notable debuts.
For me the shifts in generation for GGs and BGs were different. You see a lot of people compare EXO/BTOB who debut in 2012 with other 3rd Gen groups like BTS/GOT7/MONSTA X/SVT, but you see people comparing AOA/EXID to their 2nd Gen counterparts like Sistar/Girl's Day/4Minute
are you serious? lol 2013 was when BTS debuted
it doesn't work that way though the generation applies to both genders I think it has to do with the generation shift and that didn't happen until 2013/14 with BTS, winner, red velvet, got7 and later twice I don't know if you were around then but that's when the generation transition was really noticeable.
Exo might be kind of an exception though I get why people consider them 3rd gen. I feel it's uncommon to see an older group doing so well until now despite being around for a long time and some members are still relatively young, but at some point they were competing against big bang on music awards (album of the year for consecutive years). They were going head to head with BB on many occasions.