To clarify: when you say "when Poland was a satellite state", are you referring to post-WWII, when Poland and other eastern European states were in the Soviet sphere of influence? Or the period from 1939-1941 when the USSR absorbed the eastern half of Poland into their territory as part of the Molotov-Ribbentrop pact? I assume it is post-WWII, but there is so much movement of Polish borders around the war that it is probably worth specifying.

They needed a passport, a tourist visa, a document allowing to cross borders both with Soviet Union and individual soviet republics. There were (and are) still areas closed to tourists.

In general the visas were easier to obtain to leave the country for a fellow socialist state.