Asking 'why' anyone does anything is usually an exercise in opening a can of worms. Its a question that should be answered though; and, admittedly, I don't have an fully-detailed answer just yet. However, I would argue that not every decision is entirely rational. Sometimes circumstances coerce you to act on your instinct or emotions.

I had originally intended for their contract to be something that was done in the heat of the moment. With a swarm of negari outside, unprotected pedestrians in the street, and no magical girl in sight, what is a fairy supposed to do? 

Playing defense is always hard because an attacker only has to get lucky once and find a spot the defender isn't paying attention to. While the defender themselves typically have to split their attention and are almost solely reactive.

So a flustered fairy, who was in the area by chance, hastily makes a contract without thinking to keenly about the consequences. If there's a clear and present danger to innocent people, and leaving the scene to get help would take too long, wouldn't it be better to just deputize someone (albeit with magical powers) to deal with the problem quickly?

Am I missing something about how fairies and magical girls normally respond to incidents like that? What's standard procedure? Is there one?

Did the fairy break any rules by forming a contract in those circumstances? If so, what kind of punishment would they receive? What kind of conflict would it create?