Is there a reason why they have to be covered with foil? Not all oven run the same. I judge by the jiggle.

The pan holding your pots gets covered with foil to help prevent a skin developing during the baking process. So far as oven variance goes, of course all ovens vary and so will the baking times. I always assume the times are given for guidance, rather than being inscribed in stone. The recipe says to remove the pots when barely set - which I assume can be interpreted as judging by the jiggle. That will take generally between the 40 and 50 minutes stated, I think we can also safely assume.