I put my colonized jars into my chamber and after a couple days my cakes became fuzzy, is this cobweb? Will it contaiminate my roomn?
It's most likely the mycelium starting to colonize. It may look fuzzy before it starts to form rhizomorphs, or long ropey strands. Cobweb mold is kinda grey, not as white as mycelium. IME cobweb mold only forms after you've birthed the cakes and put them in a fruiting chamber.
Can't give you a definite answer without pictures. However, to balance out what WoodsCall said, I've seen plenty of cobweb in jars that have not been birthed yet.