Very weird. I'd give them a call and ask why they're reporting, and if they can please stop.
I'd also like to hear from the pros here how something like affects your score.
It's not a CC,.so how can it factor into your AAoA. It's also not a loan or mortgage so how does FICO rate it?
Starting Score: 600s
Big question is how are they reporting explicitly?
Are they lumped in with the revolving accounts with a term of one month? If so, they're probably effectively identical to an Amex charge card from a FICO perspective: it'll likely count in the number of cards with balances so you're right it will need to be considered for number of cards with balances.
If they aren't, then it could be something different.
There was a big push to put non-standard accounts on credit reports for some good reasons (to try to help the legions of the un/underbanked consumers), but as you intimate there's some downsides too.
I'd hope there'd be some way to exclude them from the algorithm, but it's hard to say when that would have been put in place if at all for the non-traditional history. I hope my utility bills don't suddenly start reporting as new tradelines, if they want to add the full monty 9 years I've been on the single account, well that might be a different story in my case at least. 
That's interesting.
I would pull from the bureaus directly: if it's not listed as revolving then I don't think you have to worry about the balances issue. I've never seen the utility classification previously, it's presumably new from the goal of getting non-traditional tradelines on the report... but I suspect that means the traditional FICO algorithm may unilaterally ignore them... or it might factor into AAOA unfortunately, it's just too hard to know without some clarification or anecdotal calculations using Scorewatch most likely.
On second thought, I'd probably get my Equifax report directly if any report to there, since Equifax does both a classification of debt, and also an AAOA calculation (note it might not quite be the same FICO does if FICO ignores certain tradelines, I don't know on that but it's as good as you can get really without asking FICO directly), and you can do the AAOA math yourself to see if it's included or not. That probably solves both issues, and ultimately it's what the bureaus have which counts... 3rd party monitoring can always have translation errors.
I would just pull the reports from all the bureaus they're reporting to, and like Reverate said, just check my AAoA. If it's changed (lowered), then you know it's being factored in.
I wouldn't count anything, seeing if your AAofA changed is the easiest way to tell.
eta: This is provided you knew what your AAoA was before they started reporting.
