Timewise, you're looking at this in the way we look at generations of human beings. It doesn't translate.

Art, culture and technology changes faster than humans give birth.

Within music- particularly urban genres- the sound and direction changes rapidly and a particular sound/crew/label will dominate the mainstream airwaves for a time before giving way to another. You simply can't view cultural, artistic, or technological generations along the same clear-cut general lines as you do humans. You have to look at where trends ebb and flow to define where a generation begins and ends, not some arbitrary timeline.

Musical mediums alone have undergone at least 4 dramatically different changes in the last 20 years. We've gone from the Walkman to the Discman to MP3 players to streaming services.

Doggystyle's "generation" was all but dead by the time "Life After Death" hit. Puffy and his shiny suits ran the airwaves until Hard Knock Life hit and Def Jam snatched it right back with Jay, DMX, Meth, etc. While that was bubbling, Rawkus built a sizable niche between 97-02. Those two collective entities really represent a generation unto itself. No Limit also built an empire during this timeframe.

Then you had Aftermath. Aftermath from TSSLP-The Eminem Show represents one generation of that sound, including "2001", and I'd even throw in Xzibit's Restless/MvM albums, despite being released on Loud. Once 50 and G-Unit hit, they supplanted Dre's crew as a new generation with a different sound, though still obviously an Aftermath product.

Of course you have the Neptunes and Rocafella overlapping with these, not to mention regionally dominant stalwarts like E-40 and Three Six Mafia, for example.The point is to give an in depth analysis of the last twenty years of urban music, but to illustrate that a "generation" in music really consists of pockets of mainstream visibility that can last anywhere from six months to four years, and these often overlap.