There were 2 classes of Soviet nukes in Cuba: those mounted on IRBM missiles with enough range to reach a swath of US territory & short-range, so-called battlefield nukes. Fidel wanted control over the latter so that if the Marines landed he could nuke the invasion fleet (and possibly some US port facilities).
You are correct. I was a Marine at that time and we were preparing to invade Cuba.
As a participant, I've viewed that bit of history much differently than most others. If Castro had gained control of those tactical nukes, he would have fired on the U.S. invasion fleet and Kennedy would have then destroyed the USSR. Khrushchev then realized he was dealing with two immature adolescents who would end the world as we know it, and he was the only adult in the group, so it was up to him to end the confrontation.
Over the years, JFK has been lauded for making Khrushchev back down, but I've always been thankful to Khrushchev for saving the world when two immature adolescents were hell-bent on destroying it.