Why is it "dopóki nie urosłem", and not "dopóki urosłem"

I was reading this sentence:

"Wysiadywała je i ogrzewała swoimi mięciutkimi piòrami, dopóki nie urosłem na tyle duży, że nie mieściłem się już w skorupce".

Literally translated, the text seems to read something like "She incubates them [the eggs] and warms them with her soft feathers, until I do not grow up big enough, that I do not already fit myself in the shell."

I can tell the highlighted text is saying the same thing as " I grow up", but with some strange negative case usage happening here. Is there a reason why this is the case? Are there any other rules or examples that follow this trend? I know this sentence is not the best example, apologies in advance.