Recent embedded applications such as Autonomous Driver Assistance Systems (ADAS) require large computational resources that increase the need for HW accelerators, e.g., in system-on-chip-based platforms. Synthesising optimal task/data mappings and schedules for such platforms becomes increasingly challenging, even more in safety-critical contexts. For designing real-time heterogeneous systems, response time computation and the resolution of task mapping problems are required as demanded in the WATERS 2019 challenge. Our contribution to address the challenge is to extend a design space exploration (DSE) formulation of mapping applications on MPSoCs architectures to consider DMA-based data (pre)-fetching. The approach is performed in two steps. First, we determine task mappings to a heterogeneous MPSoC platform using a multi-objective evolutionary algorithm (MOEA)-based DSE. In order to check the feasibility of an allocation, and to rate its quality, we use a SMT solver to construct schedules whose latency is close to the achievable minimum. Our task response time analysis considers the effects of memory access times and DMAs to supply the SMT scheduler with data fetching latencies. The MOEA-DSE, the SMT scheduler, and the response time calculation are integrated into the AutoFOCUS 3 tool that has been extended with an importer for the AMALTHEA model that specifies the challenge use case.