In order to get reimbursed from an FSA, you probably have to provide the name, address and tax number of the provider. The IRS will naturally be looking for matching income on their return.
If care is provided in your home under your rules, they are your household employee and you are required to issue a W-2 and pay household employer's tax if you pay more than $2200 per year.
If you pay less than $2200 in your home, or if care is provided in the provider's home or place of business, you have no other tax responsibilities. How the provider files and what their tax will be depends on their overall financial situation.
