You are correct, they all start out red, with the exception of the ones minted in 1943. The picture you have posted would be classified with a color of brown. A red cent is nothing more than a cent that has retained it's original red color as it came from the mint.
From Cassell's Dictionary of Slang by Jonathon Green, pg. 1182. red cent n. (also blue cent, red copper, red penny, white quarter) [mid-19C+] (US) a trivial amount of money, usu. in phr. not a/one red cent, absolutely nothing of (cf. CENT n.) [the copper colour of a cent; the blue cent may refer to the blue cardboard ration tokens issued in US during WW2 as payment for processed foods (meat tokens were red)] * OPA Rations tokens (red and blue)