The fact that there were missiles in Turkey was never really a secret. Anyone reading American newspapers would have known it was happening (e.g., "Turkey to Get IRBM Base; Soviet Complaint Expected: Accord Reached at NATO Headquarters -- U.S. to Supply Weapons" New York Times (11 Oct 1959), A1).

The fact that the US relied heavily on foreign basing of missiles and bombers was well-known and public at the time, even if many of the specifics were not. But the press at the time confirmed there were Jupiter IRBM missiles in Turkey, Italy, and several other locations. It is a kind of a hard thing to hide; Jupiters are not particularly stealthy.

As an aside: it was Eisenhower who agreed to put the missiles in Turkey, as an aside, and JFK was not very fond of the idea, but various crises, diplomatic issues with Turkey, and other distractions kept him from altering the plan. When the Soviets put missiles in Cuba, Kennedy definitely saw it as a response to the missiles in Turkey and can be heard on the tapes at times remarking bitterly about how he had known the Turkish Jupiters would be a problem. See Larry Loeb, "Jupiter Missiles in Europe: A Measure of Presidential Power," World Affairs 139, no. 1 (Summer 1976), 27-39.