Yeah, that’s when the tech first developed, but it wasn’t common use until much much later.
In the 90s, cell phones were still rare, and even as they became more popular, they didn’t have a QWERTY keyboard or a decent size screen until the blackberry was released in 99.
The first real texting trends that I saw in the US came around 98-99 as some new pagers came out with the ability to send sms and had qwerty keyboards, but they were only used by small groups of people within their social/business circles.
I’d forgotten how late the qwerty keyboard came out. I didn’t get one until 2008 I don’t think - iPhone 3G. I don’t think predictive text was common/standard until 2003ish. Having to press 7 four times to get an S was such a ballache!
IIRC When I got my first mobile in 1999 I could send 10 very short messages a day max. I only had one other person I could text. It wasn’t until 2002ish that texts became a common thing. It wasn’t until 2004ish that the ridiculous limit was removed.