The evolutionarily dominant strategy is commonly called “Tit-for-tat” - basically, cooperate if and only if you expect your opponent to do so.

That strategy is neither evolutionarily dominant nor "tit-for-tat". Tit-for-tat is applicable in the Iterated Prisoner's Dilemma with unknown duration and involves cooperating on the first round thereafter doing whatever the opponent did in the round before the current round. As the name implies it is somewhat like a specific implementation of "eye for an eye".

As for evolutionary dominance the strategy "cooperate if and only if you expect your opponent to do so" is strictly worse than "If cooperating gives the expected result of your opponent also cooperating then do so unless they will cooperate anyway". ie. Your proposed "completely-not-tit-for-tat" strategy cooperates with CooperateBot which is a terrible move. ("CooperateBot" may represent a much smaller or lower status monkey, for example.)