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, as many people cannot afford to pay so much in advance for a travel. 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 the 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.