I don't know anything about that brand, but...
non-toxic is certainly a good sign! I would read the instructions and see what it says about breathing the fumes. That is what you are worried about, unlike worries about kids who might chew on something with the paint on it. Also, you can check it out for yourself as to how strong the fumes are. No matter how non-toxic it is, I would let it air out in a different room or outside, for at least several days. After that, close it up in a small area (like a closet or even in a plastic bag) overnight, and see if the fumes are still strong. Once there is only a small odor after being closed up in a small area, it is probably fairly safe. But I would still give as much ventilation as possible inside the cage for many weeks after installing it. It may be entirely safe, but better to be too conservative than to take a chance.