The IRS considers anything in box 7 of 1099-MISC to be self employment income. Enter the 1099-Misc income, at Other Common income / income from a 1099-MISC . TurboTax (TT) will complete Schedule C or C-EZ for you and allow you to deduct any expenses associated with this income. These types of payments are frequently done this way. Your "employer" is not the only one.
The $608 is all self employment (social security and medicare) tax. None of it is income tax.
