Manhattan Project was 1942 ~ 1946, while McCarthyism was 1947 ~ 1959.

Contributing to the rise of McCarthyism was: >a growing obsession with perceived dangers posed by internal subversion in general and Soviet and Communist Party espionage in particular, fueled by reports, some public and some held within the government, of Russian spy operations in North America, accompanied by a new Communist "hard" line that echoed general Cold War tensions;

So, correct: The Manhattan Project(full of academics, some(many?) of whom happened to be liberal) was as you put it "chock full of soviets" and the natural reaction to that realization was to clamp down on liberals.