Recent advances in self-supervised learning (SSL) for point clouds have substantially improved 3D scene understanding without human annotations. Existing approaches emphasize semantic awareness by enforcing feature consistency across augmented views or by masked scene modeling. However, the resulting representations transfer poorly to instance localization, and often require full finetuning for strong performance. Instance awareness is a fundamental component of 3D perception, thus bridging this gap is crucial for progressing toward true 3D foundation models that support all downstream tasks on 3D data. In this work, we introduce PointINS, an instance-oriented self-supervised framework that enriches point cloud representations through geometry-aware learning. PointINS employs an orthogonal offset branch to jointly learn high-level semantic understanding and geometric reasoning, yielding instance awareness. We identify two consistent properties essential for robust instance localization and formulate them as complementary regularization strategies, Offset Distribution Regularization (ODR), which aligns predicted offsets with empirically observed geometric priors, and Spatial Clustering Regularization (SCR), which enforces local coherence by regularizing offsets with pseudo-instance masks. Through extensive experiments across five datasets, PointINS achieves on average +3.5% mAP improvement for indoor instance segmentation and +4.1% PQ gain for outdoor panoptic segmentation, paving the way for scalable 3D foundation models.