Contagion Engine

An ability that triggers "Whenever you proliferate" triggers even if you chose no permanents or players while doing so.

Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.

Players can't respond between the first and the second proliferate actions.

As Contagion Engine's activated ability resolves, you'll complete an entire proliferate action, then you'll complete a second proliferate action. You may choose different players and/or permanents, or different counters on those permanents, when you proliferate the second time.