The Soviet made that reaction out of their own fear that Reagan would attack them first.
One should note here the comparison to the German military mindset at the outset of World War One. Germany saw itself in an inferior position - and increasingly so - when confronted with France and Russia combined. From the viewpoint of Fin-de-siecle military planners, this indicated a certainty of a Two-Front-Attack at some point on the future.
Instead of pursuing a policy of de-escalation, the assessment drove them to with hindsight unreasonable conclusions. The first is to rather deliberately risk war as long as conditions seem at least partially favourable - or actually just less unfavourable than in the future. The second is feeling forced by the circumstances to handle the outbreak of the war in a most aggressive way, i.e. DOWing France and the implementation of the Schlieffen-plan.
This WW3 is basically the same game with bigger guns. Like Germany, Sovjet assessment of its own strength had to come to a conclusion that its standing could only worsen and make a NATO-attack under unfavourable circumstances more probable in the future. ITTL the outcome is similar to 1914. If the 1910s had worked out as OTLs 1980s, we would have been spared a lot of a mess (and me).
Kennedy had read Tuchman's "The Guns of August" prior to the Cuba crisis and reportedly drew motivation to avert war from it even when confronted with Sovjet aggressiveness.
Perhaps the Sovjet leaders of this timeline read Fritz Fischer accusing "Griff nach der Weltmacht" (literally German's bid for world power, published in English as
Germany's Aims in the First World War) and misused it as a blueprint.
On a more serious note, consider the psychological phenomenon called "groupthink" in the Kremlin and you are on the road to war.
Sorry for the excursion, but I just wanted to point out that stupidity on that scale has happened before and the Sovjet path is despite its madness not as implausible as it seems.
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Another word on Warsaw-Pact war plans. As far as I could get my hands on them, the prime source for them are deliberate Polish leaks post-1989. This is far from an assessment of the full scale of possible Sovjet reactions and plans, IMHO. The difference that this timeline delivers a long-time planned Sovjet provocation with their standard-rhetorics instead of the usual base of Sovjet maneuvres ("evil NATO surprise attack") might make the difference already.
Besides, the massive conventional Warsaw Pact superiority on the European battlefield makes a quick escalation to a nuclear scale which effectively nixes this superiority (and pretty everything else along with it) seem rather stupid, even giving WW3-standards. For the first three days of this timeline's war, the Sovjet leadership will probably try for a push to the Rhine, ergo enforcing their ultimatum, then see (hopefully in their eyes) NATO dissolve and negotiate from a newly-won position of strength. Again, a parallel to the German pre-1914-assessment that driving the later-to-be Entente to the edge of war and making them shy away from it would result in the superior alliance breaking apart quickly.
I should stop now.