"Tankie" does not come from Tiananmen Square, that is a common misconception. The term "tankie" is 33 years older than the Tiananmen Square massacre.
It originated to describe people who supported the 1956 Soviet Union military intervention in Hungary. Stalin sent in a bunch of T-35 tanks to crush the Hungarian Revolution. He was successful, and thousands of people died in the process.
Ever since then, "tankie" has been used as a derogatory term against Stalinists, Marxist-Leninists, communists, and leftists in general.