Deep learning models for medical image segmentation often struggle when deployed across different datasets due to domain shifts - variations in both image appearance, known as style, and population-dependent anatomical char-acteristics, referred to as content. This paper presents a novel unsupervised domain adaptation framework that di-rectly addresses domain shifts encountered in cross-domain hippocampus segmentation from MRI, with specific empha-sis on content variations. Our approach combines efficient style harmonisation through z-normalisation with a bidi-rectional deformable image registration (DIR) strategy. The DIR network is jointly trained with segmentation and dis-criminator networks to guide the registration with respect to a region of interest and generate anatomically plausible transformations that align source images to the target domain. We validate our approach through comprehensive evaluations on both a synthetic dataset using Morpho-MNIST (for controlled validation of core principles) and three MRI hippocampus datasets representing populations with varying degrees of atrophy. Across all experiments, our method outperforms existing baselines. For hippocam-pus segmentation, when transferring from young, healthy populations to clinical dementia patients, our framework achieves up to 15% relative improvement in Dice score compared to standard augmentation methods, with the largest gains observed in scenarios with substantial content shift. These results highlight the efficacy of our approach for accurate hippocampus segmentation across diverse populations.