Will they set up the tent I reserved when I arrive?

Yes, but it depends on the campsite operator:

Vertice Patagonia campsites (Grey, Paine Grande, Dickson, Los Perros): If you reserve a tent as part of your booking, it will be set up for you when you arrive.

Las Torres Patagonia campsites (Serón, Francés, Cuernos, Chileno, Torres Central & Norte): Tents are only pre-set if you book the Premium campsite accommodation type. If you choose a different option, a tent will not be included.