Yes, you need to apply for reimbursement, especially when having received an advance payment of 80%. The prepayment is only a support structure for travels that cost more than 200 EUR. Nevertheless, you have to apply for official reimbursement within 6 months after travel. 

The travel department has to decide if your trip has been conducted according to all regulations of Federal law, and they will reimburse the rest of the travel expenses (20%). If you did not need the advance payment or spent less on the travel than anticipated, you need to pay the advance payment or the difference back.