They are doing it right. if you are a W-2 employee, and additional pay should be on your W-2, not a 1099*.
If this employer was your only side business client, you effectively no longer have a business. Your expenses, for this additional work can only be deducted as job expenses on schedule A and not business expenses on schedule C.
You are allowed to deduct your job expenses, subtracting what you were reimbursed (do not subtract your reimbursement if it was included on your W-2 as taxable income). TurboTax completes form 2106, which then carries to Misc itemized deductions on Schedule A. The problem with this is that you only get to deduct that portion of your misc deductions that exceed 2% of your AGI. and then only if your total itemized deductions exceed the standard deduction. (2% rule explained:
https://ttlc.intuit.com/questions/2902781-what-is-the-2-rule)
In TurboTax, enter at:
Federal Taxes Tab
Deductions & Credits
-Scroll down to:
-Employment Expenses
-- Job related expenses
*Depending on how unrelated the activity is to your regular job, it might be OK if they gave you a 1099-Misc, instead of putting it on your W-2. That would allow you to deduct your expenses, directly. But, you would have to pay the employer share of FICA (7.65% of the pay).
Most of the complaints, we see in this forum, are for the opposite situation. The employer pays the extra work on a 1099-Misc, forcing the employee into paying his own FICA and paying more for tax preparation.