Mid nineties to early 2000s was when modems were mainstream. People usually got their email using POP3, dialing up either manually or automatically on a schedule. Email clients were designed around offline use, as were newsreaders. Outbox was a thing; it was where your emails went until you went online next.
I was misremembering a bit because I got cable to my house in about 1996 but I don't think I got broadband for a few years after that. I'm pretty sure I had it by 2000 or so but probably not much before that.
I had a modem starting in about 1984 or so but they were certainly still a geek thing for consumers at that point.