EXO started as 2nd Gen Group and their enorme success in the foreign market (especially China and SEA) and overtaking popular 2nd Gen groups in Korean charts set a new standard and opened the 3rd gen. Therefore, it’s correct to consider EXO as first 3rd gen group.
However, when I praise the 2nd Gen I also include EXO in my mind, even when they’re officially considered as 3rd gen group. I suspect that people who mistake them in 2nd Gen are older kpop fans that experienced their debut in 2nd Gen era (like me).