From what I see and think, you can tell what generation it is based on the groups, music sound or a big occurrence of events. Like, the 1st generation includes the very first K-Pop idols/groups, the beginning of K-Pop (i.e: S.E.S, Shinhwa, PSY, Fin.K.L, Seo Taiji & Boys, H.O.T, Baby V.O.X, Sechskies) and as far as I know the 1st generation goes from 1992 until 2002, which I suppose was the year where many of the 1st generation groups started being inactive, went on hiatus (probably due to the military), which lead to the 2nd generation (i.e: Super Junior, BigBang, Brown Eyed Girls, Epik High, Girls' Generation, SHINee, 2NE1, TVXQ, 4Minute, BoA, Wonder Girls, U-Kiss, T-ARA, miss A, SS501, After School, KARA, Coed School) taking over from 2003 until 2012.

The 2nd generation was the time where the Hallyu wave started, and in 2012 was when PSY helped the wave reach its peak. More international concerts started happening more often, debuts in China and Japan started to be a "thing" in the industry. The 3rd generation starts when, once again, a big part of the previous generations groups start disbanding or going on hiatus due to military enlisting.Leading to the 3rd generation (i.e: BTS, TWICE, WINNER, Red Velvet, Mamamoo, BLACKPINK, GFriend, GOT7, Monsta X, Seventeen, KARD, AKMU, CLC, iKON, Day6) from 2013 till now.

I believe the generations change when a "big" turn happens in K-Pop, for example, the music sound. And something funny I've noticed is that some groups are the "bridges" between generations. For example, TVXQ is the bridge between the 1st and the 2nd generation because at the beginning they were like a mix of both generations. EXO is the bridge between the 2nd and 3rd generation for the same reason, and also because most people never know where to place them,same for G(idle) i think their part of the3rd generation. also think that the generations are separated once something big happens in the industry.

When 1st gen started, it was something new. And when it ended the "big turn" was the sudden flooding of debuts. More companies started doing the whole training system and decided to debut their groups around this time. And when PSY got famous in America in 2012 was the big turn that was needed to make a shift & start a new generation. After PSY's success in America, a new generation starts. The one that gets to enjoy the attention PSY brought to the genre/industry and now the groups of this generation are starting to be more international, more western. Companies are starting to focus more on the Western market.