It's hard to remember really, but automatic downloads would have been considered quite a misfeature by lots of user sites, in an era of intermittent, metered internet connections.
As I recall, rpm could list dependencies but not automatically fetch them. Full apt-style recursive downloads weren't a thing until yum from Yellowdog (a PowerMac-specific clone of RedHat) and urpmi from Mandrake, both of which arrived in late 1999 or early 2000-ish.
RedHat eventually started using yum as well, but not until around 2002.
Certainly, in the late 90s, apt was king. Debian was struggling badly with their internal processes at the time, though, so they didn't benefit as much as they otherwise might have.