Not hours. An ICBM has a speed of about 7km/s. So it's a question of minutes in any case. Also, I'm not sure Americans could have detected a lauch immediately in 1962 (they later spent enormous ressources to build NORAD right for this purpose). So the reaction time begins only when rockets are detected by radars, when they are already approaching their targets. That means the reaction time is the same whether the rockets come from Siberia or Cuba.
Not quite, though almost. A rocket flying from Siberia needs something between 20 and 30 minutes to hit parts of the continental US (other than Alaska). A missile flying from Cuba could hit within five minutes or less. 20-30 minutes, in those days of permanent readiness for everything, still left enough time to evacuate the senior government, scramble a lot of aircraft and move some troops out of the way. Missiles flying from Cuba (or indeed, submarines) negated that possibility. So the missiles from Cuba were a threat, even if it is not a major strategic difference.