I knew Sino-Soviet relations went sour soon after Stalin died and things heated up and there were years of border clashes. That nukes were used is news to me. Do you think both sides used nukes or just one? I think the Soviets had more advanced technology and the Chinese didn't "officially" test a nuke until sometime in the 1970s. Who knows what unofficially happened.
Things went very sour when Mao told Kruschev he was willing to trade half of China's population to win a nuclear war with the US. The Soviets realized they were dealing with a madman and promptly pulled out all the nuclear scientists who were helping the Chinese. Things really got ugly with the border skirmishes in the late 60's-early 70's, but this is the first time I've heard it suggested that nukes were used. If it's true, I'm not surprised that neither side wants to talk about it.
My guess, based on what happened to us in Korea, is that the Red Army in Siberia was facing more of an invasion than a minor skirmish, and fearing an overrun, the Kremlin authorized using tactical nukes. It's the same doctrine NATO planned for in Western Europe in the event of war with the Warsaw Pact.
Knowing something about Chinese and Soviet tactics of the era, I suspect that all the events were Soviet in origin.
However, I'd just be guessing at it, like anyone else.
FYI, China had the A-bomb by 1964 and the H-bomb by 1967: http://nuclearweaponarchive.org/China/ChinaTesting.html