We study fine-grained referring image segmentation via a decoupled reason-then-segment pipeline. A vision-language model (VLM) receives an image and a natural-language query, reasons about the scene, and emits structured spatial prompts: a bounding box plus two interior keypoints for every referred instance. A frozen promptable segmenter (SAM 2) converts these prompts into high-quality masks. Within our GenSeg-R1 framework we finetune Qwen3-VL models (4B and 8B parameters) using Group Relative Policy Optimization (GRPO), requiring no supervised reasoning-chain annotations. On RefCOCOg validation our best model (GenSeg-R1-8B) achieves 0.7127 cIoU and 0.7382 mIoU, substantially outperforming the corresponding Qwen3-VL Instruct baselines (+15.3 and +21.9 points, respectively) and surpassing Seg-Zero-7B [3] by +3.3 cIoU under identical evaluation. We further introduce GenSeg-R1-G, a variant trained on GRefCOCO [9] with a SAM 2 in-the-loop reward that directly optimizes mask quality. On GRefCOCO validation GenSeg-R1-G achieves 76.69% target mIoU with 82.40% accuracy on negative (no-target) prompts, substantially outperforming Seg-R1-7B and Seg-Zero-7B, which lack no-target detection capability. On ReasonSeg test, GenSeg-R1-4B reaches 68.40% mIoU, surpassing Seg-Zero-7B by +7.0 and Seg-R1-7B by +10.7 points.