Let us begin by acknowledging that Marxists indeed advocated that all the world should become Communist, but not by hostile takeover. Rather, they advocated a series of national revolutions around the globe which would allow the victorious workers ultimately to join together as one, abolishing the very idea of nationhood.
Indeed, when the Russian Revolution succeeded, a fierce debate erupted over whether it was legitimate to try to build Communism in one country without the support of other revolutions elsewhere. A counterattack by defenders of the old order was mounted by the “white Russians” (contrasted with the “red” Communists) aided by such foreign powers as Great Britain, Japan, France and the United States (which sent troops that never actually entered combat). In such circumstances, it is understandable that the new government should decide to press ahead without outside support, and that it would later try to generate revolutions abroad from outside.
The idea of a threat of world conquest by Communism was usually based on the experience of the period after World War II, when the Soviet Union imposed a series of Communist governments on the often unwilling populations of the countries they had occupied. They insisted that they were not conquering but liberating these nations from the shackles of capitalism. Having extended the bounds of the Revolution beyond the borders of the USSR, it was unthinkable that they should retreat and allow power to fall back into the hands of their bourgeois masters. Probably more important, however, was the desire of the Soviet Union to surround itself with a buffer of sympathetic, easily controlled states which could protect it from another invasion of the sort Hitler had carried out to such devastating effect.
The West viewed this move as purely an aggressive one, a forerunner of further campaigns of world conquest, and viewed the Soviet-backed Chinese revolution and the Chinese-backed Korean War which followed as proof of a general program of Communist expansionism, as was the Chinese conquest of Tibet. This was strong evidence, not lightly dismissed.
Yet the USSR did not in fact invade and “take over” China, and by 1960 had abandoned its former ally, and the North Koreans did not fall under the sway of China, stubbornly refusing to follow the Chinese lead to this day. The simple model of military conquest which dominated Western rhetoric about Communism during the Cold War was often a misleading guide to events, prompting American Presidents, for instance, to identify the Vietnam War as a Chinese project when it was in fact a civil war in which the Vietnamese Communists–both then and later–were often hostile to the Chinese. The invasion of Cambodia by the Vietnamese is another contest seen as an instance of Communist aggression when in fact the more liberal Vietnamese might have been able to prevent the genocide carried out by the radical–not to say insane–Communist Khmer Rouge if the Americans had not driven them out.
The Vietnam War was enormously prolonged because of the American conviction that the fall of Saigon would be swiftly followed by the fall of Laos, Cambodia, and much of the rest of Southeast Asia in a “bloodbath.” When Saigon did fall and the Americans left, many people suffered; but the predicted bloodbath and fall of “domino” states did not ensue. The Vietnamese were far more nationalist than expansionist, whatever their political beliefs.
Yet it would have been a foolish political leader indeed who did not take seriously the threat of invasion by Communist troops. Because of the secrecy of the Russians and the paranoia induced by the nuclear arms race fueled by both sides but led most often by the Americans, this threat was often wildly exaggerated. Hindsight tells us that much of the Cold War rhetoric envisioning the Soviet Union and its allies as bent on the military conquest of the rest of the world was mistaken; but their non-military and indirect military interventions posed serious threats that help to explain the inflamed rhetoric.
However the history of actual Communist states is analyzed, the notion of forcible imposition of Communism on unwilling majorities is certainly contrary both to Marx’s beliefs and those of most Marxists.