While I've seen other potentially-applicable sections quoted elsewhere, a traffic-research app used by paid contractors of a company would seem to meet both the "Internal Use Application" definition, and the "Permitted Users" definition.
Further, some stories have reported that Facebook says they acquired such parental permission for the minor participants.
Additionally, the minimum age for non-agricultural workers is 14 anyway, so even then they're in the wrong and can't legally hire 13-year olds as contractors or employees. There's also several other rules in the FLSA pertaining to workers under 18 including minimum wage. I have a sneaky suspicion $20 per whatever period it is (unless said period is a few hours) is going to be under that wage.
Not to mention there's a whole lot more can of worms being opened specifically around minimum wage and recording hours that I highly doubt either Facebook or Google were actively managing.
I've never seen that relationship result in anyone being called a contractor and I've signed too many film contracts. I don't know where OP is getting this notion.
Here you can see a VentureBeat reporter – and one who is actually a member of the California State Bar of Attorneys – raise some of the same questions as I have:
https://venturebeat.com/2019/01/31/the-odd-reason-apple-kill...
Late in this article, you can see Facebook's statement that all minors who participated did so with signed parental consent forms:
https://gizmodo.com/facebook-is-paying-teens-to-install-a-re...
Facebook's statement: "Key facts about this market research program are being ignored. Despite early reports, there was nothing ‘secret’ about this; it was literally called the Facebook Research App. It wasn’t ‘spying’ as all of the people who signed up to participate went through a clear on-boarding process asking for their permission and were paid to participate. Finally, less than 5 percent of the people who chose to participate in this market research program were teens. All of them with signed parental consent forms."
You are a "contractor" if you are providing services under a contract. A contract exists whenever there is a definitive agreement to exchange valuable considerations – even in the absence of a written, signed contract.
But the sign-up for these apps might have included an explicit "signing" phase! (It's even possible that FB/Google asked for participants' SSNs, just in case any payments went over $600.)
(And if they’re under any sort of confidentiality agreement or other conditions on their app usage, they fit under the Apple terms’ concepts of “Permitted Users” and “Internal Use” even better.)