While it is possible to blame the US and its policy of containment for the globalization of the Cold War during this time, it is also possible to blame the Soviet Union.
Of course, the US did go around the world intervening in other countries whenever it felt that communism might be spreading. This zeal for containing communism could be blamed for such things as the interventions in Iran and Guatemala in the early 1950s and the Vietnam War. In this way, we can claim that the US spread the Cold War through its efforts at containment.
However, we can equally say that the Soviet Union and communists more generally globalized the Cold War by their efforts to expand. One of the most obvious examples of this comes at the beginning of the time period that you ask about. The Korean War in 1950 represented an extension of the Cold War that was caused by communist aggression. The same is true of an event at the end of the time period. The Soviet invasion of Afghanistan in 1979 was equally caused by a desire to spread communism and to maintain it where it already was.
Thus, it is not really possible to objectively blame one side more than the other for the globalization of the Cold War.