Device-free crowd-counting using WiFi Channel State Information (CSI) is a key enabling technology for a new generation of privacy-preserving Internet of Things (IoT) applications. However, practical deployment is severely hampered by the domain shift problem, where models trained in one environment fail to generalise to another. To overcome this, we propose a novel two-stage framework centred on a CSI-ResNet-A architecture. This model is pre-trained via self-supervised contrastive learning to learn domain-invariant representations and leverages lightweight Adapter modules for highly efficient fine-tuning. The resulting event sequence is then processed by a stateful counting machine to produce a final, stable occupancy estimate. We validate our framework extensively. On our WiFlow dataset, our unsupervised approach excels in a 10-shot learning scenario, achieving a final Mean Absolute Error (MAE) of just 0.44--a task where supervised baselines fail. To formally quantify robustness, we introduce the Generalisation Index (GI), on which our model scores near-perfectly, confirming its ability to generalise. Furthermore, our framework sets a new state-of-the-art public WiAR benchmark with 98.8\% accuracy. Our ablation studies reveal the core strength of our design: adapter-based fine-tuning achieves performance within 1\% of a full fine-tune (98.84\% vs. 99.67\%) while training 97.2\% fewer parameters. Our work provides a practical and scalable solution for developing robust sensing systems ready for real-world IoT deployments.