My dad paid my tuition directly to the university. If my employer reimburses tuition, will the tuition paid directly to University by my dad considered as gift to me?

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Q. Will the payment made by father in advance directly to the university be considered as Gift to me?

A.  No. Tuition payments made directly to a college are not considered gifts for tax purposes (the education exception*). Furthermore, if you are your parent's dependent, the money is considered support not a gift. 

Q.  If the employer reimburses, do I have to pay tax on it?

A. Probably not. Employers are allowed to pay up to $5250 of tax free tuition**, for an employee. The fact that your parent made the original payment is not relevant.  So, it depends on how your employer handles the reimbursement (and whether their tuition reimbursement plan meets IRS rules). 

*References: https://www.thebalance.com/what-gifts-are-not-subject-to-the-gift-tax-3505684 

 https://www.schiffhardin.com/insights/publications/2018/faqs-on-the-use-of-the-gift-tax-medical-and-tuition-expense-exclusion

**Any amount reimbursed by tax free assistance is not eligible for a tuition credit or deduction.