They did have ways to detect nuclear incidents before then. Vela satellites for example. They seem to have been more tuned for detecting nuclear bombs vs generalized fallout however. Maybe others can speak more towards this.

The last of the Vela satellites were shut down in 1984 or 1985 (I've found conflicting sources on this) but in any case, before Chernobyl (April, 1986). They were replaced by other systems of course but as others have pointed out, those were never designed to detect fallout. Bhangmeters look for a characteristic double-flash of light from atmospheric nuclear detonations.

Yeah, the Vela sats could spot nuclear detonations, but didn't sniff for trace isotopes or anything like that. They were in way too high an orbit for any traces to make it to them anyhow.

The bhangmeters on Vela satellites were to detect atmospheric detonations: they exploit some odd optical characteristics of the fireball.

They did have gamma, neutron, and X-ray detectors too but I’d guess those were also tuned to detect detonations rather than small background changes. That might not be feasible from so high up and it would square with the Velas’ role in discovering gamma-ray bursts.