The increasing complexity of real-time applications on heterogeneous multicore systems presents significant challenges in meeting both performance and energy constraints. Existing task allocation methods often rely on static or simulation-based approaches that lack runtime adaptability and hardware validation. In this work, we present Adaptive Task Allocation Strategy (ATAS-HM), which combines offline Worst-Case Execution Time (WCET) profiling with runtime feedback-based reallocation to assign periodic real-time tasks across heterogeneous cores dynamically. Implemented on a Xilinx Zynq UltraScale+ MPSoC, ATAS-HM achieves up to 2.3× faster response times compared to the State-of-the-art strategy and up to 100× lower energy consumption compared to baseline methods. These results demonstrate the practical effectiveness of ATAS-HM for energy-aware, real-time task scheduling in heterogeneous embedded systems.