The large hadron collider (LHC) will undergo a major upgrade starting in 2025 toward the high luminosity LHC (HL-LHC) to increase the instantaneous luminosity by a factor of 5 to 7 compared to the nominal value. The Phase-II Upgrade (2025-2027) will require the trigger and readout electronics of the ATLAS experiment to operate with the stringent conditions imposed by the HL-LHC. During this upgrade, both on- and off-detector readout electronics of TileCal will be completely replaced with a new data acquisition which will provide full-granularity information to the ATLAS trigger system. The compact processing modules (CPMs) are responsible for the LHC bunch-crossing clock distribution toward the detector, configuration of the on-detector electronics, data acquisition, cell energy reconstruction, and data transmission to the Trigger and Data AcQuisition interface (TDAQi) boards. This article introduces the design of the CPM for the ATLAS Tile Calorimeter Phase-II Upgrade and the results and experiences with the first prototypes.