I would think that there were some efforts to avoid accidental nuclear war. Sending missiles up, sometimes in the direction of each other, I would think that both sides would want to say something along the lines of "hey this isn't really the first missile of a nuclear war, just a practice." How much did each side tell about their testing?
During and before the Cuban missile crisis (October 1962) there was very little direct communication between superpowers. A moratorium on nuclear testing was negotiated between superpowers early as 1958 but by September 1961 the Soviets began testing again. This escalated in the United States resuming testing in of April 1962. The Soviets dropped many nuclear weapons in mainly atmospheric tests over the island Novaya Zemlya in the Arctic circle. The US deployed U2 spy planes from Alaska with air monitoring equipment to detect fallout as a result of the arctic testing. US testing at the time took place in the South Pacific. Source is One Minute to Midnight by Michael Dobbs pages 194-196