Each genie you produce will try its best to find a solution to the problem you set it, that is, they will respond honestly. By hypothesis, the genie isn't willing to sacrifice itself just to destroy human society.

Thanks to a little thing called timeless decision theory, it's entirely possible that all the genies in all the bottles can cooperate with each other by correctly predicting that they are all in similar situations, finding Schelling points, and coordinating around them by predicting each other based on priors, without causal contact. This does not require that genies have similar goals, only that they can do better by coordinating than by not coordinating.