Tom was insistent because he was gung-ho for the deal for all the reasons he said in his meeting after he came back from CA. And, I'm not sure Genco would have picked up on Barzini being behind the deal. In the novel, Vito says of the Sol meeting, "What he will propose is an infamia." So, it was credible for Vito (and probably Genco) to associate such an "infamia" with Tattaglia, whose business, prostitution, was another "infamia."