CMS is the BARE MINIMUM that you should be paying, especially if you are on a low wage. It's unlikely to cover a fair share of her costs.
If you offered less than the CMS rate, then you are a CF, and he is absolutely right to have gone to the CMS to enforce a fair payment.
Sorry, can't make head nor tail of him paying less than needed, but also you managed to save 80% of it! Makes no sense at all. In fact, reading between the lines, it sounds as though his higher wage significantly subsidised your household, and now you're upset that you're being expected to pay your own way, including a fair contribution towards your daughter's costs.
On the face of it, it seems like he's being entirely reasonable, and you entirely unreasonable. I don't understand why you would have a problem with him contacting CMS, unless you were planning to shirk your responsibility to pay reasonably towards your daughters costs? If you were planning on doing the decent thing and paying anyway, it makes no difference, does it?