In the atheistic universe, those behaviours may be at odds with one another, because the rules are not guided; they do not have an aim. They may optimise for some goal on the individual, or even the group level, but there is no reason why they should do so in an efficient manner; a puppet universe may include humans who oppose each other.

You are treating puppet and zombie as equivalents, but they are not. Rational deterministic agents may or may not succeed in co operating. Co-operation is probably the outcome that ideal rational agents would tend to , but non ideal agents face barriers to co operation. Puppets in a theistic universe may or may not co-operate depending on what the Puppetteer wants: some Purposes are served by struggle. Maybe the Puppetteer is a Nietzchian , who wants conflict and struggle to develop strength.

In the theistic universe, the presence of an omnipotent, omniscient being suggests that there is some purpose to the universe. If all people are puppets, then, it is to be expected that all people work tirelessly towards a single goal, without opposing each other.

Puppets may or may not oppose each other, zombies may or may not oppose each other, free agents may or may not oppose each other. There's nothing you can deduce.