In distributed quantum applications such as entanglement distribution, precise time synchronization and efficient time-tagged data handling are essential. Traditional systems often suffer from overflow, synchronization drift, and storage inefficiencies. We propose a modular Time Tagging (TT) agent that uses a 1 pulse per second (PPS) signal from White Rabbit (WR) devices to achieve network-wide synchronization, while applying real-time calibration, overflow mitigation, and compression. A live two-lab entanglement distribution experiment validated the system's performance, achieving synchronized coincidence detection at 25,000 counts/sec.