This also coincided with the fall of Netscape and its eventual purchase by AOL in November 1998. The dot-com bubble that people actually remember got started when that bust hit its nadir (right around the Netscape purchase), and really kicked into high gear a year later in the fall of 1999. I think that what happened is that Netscape's purchase and the subsequent recovery of Internet stocks is what convinced entrepreneurs & VCs that the Internet was here to stay, which led to a flood of capital in and a frenzy of entrepreneurial activity, and then once all their products started hitting the market 6-12 months later the public took notice and the dot-com bubble really took off.
There will likely be a similar effect with crypto as all the ICOs - the ones that are not scams, at least - actually start releasing their products for people to use. Crypto is bubblier than dot-coms because everything is bubblier now; capital markets are thoroughly globalized, and there's more capital sloshing around.
The dot com bubble didn't have a contraction like that before it popped. That was the pop.