That's right, 1999 was the release of her first album (Baby One More Time). I think the reason some feel like it must have been the mid-90s is that she went from that to the first major scandals (marriage, divorce and a shift in her musical style) as well as her first Greatest Hits album by 2004.

Her next album after that (along with the head shaving incident and being placed under the custody of her manager-dad) was 2007, so most people's memories of her as a "sexy teen idol" are likely from her 1999-2003 period, which in retrospect probably felt a lot longer, especially with the overlap of other young women pop stars in the same period (e.g. Christina Aguilera started in 1998).

For the record, neither I nor the person I replied to said 1994 (unless they edited their post). I was thinking 97 or 98, so was still off, but at this point in my life being off by a year or two feels pretty damn close ;-)