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The functional organization of the hippocampus mirrors that of the cortex, changing smoothly along connectivity gradients and abruptly at inter-areal boundaries. Hippocampal-dependent cognitive processes require flexible integration of these hippocampal gradients into functionally related cortical networks. To understand the cognitive relevance of this functional embedding, we acquired fMRI data while participants viewed brief news clips, either containing or lacking recently familiarized cues. Participants were 188 healthy mid-life adults and 31 adults with mild cognitive impairment (MCI) or Alzheimer's disease (AD). We employed a recently developed technique - connectivity gradientography - to study gradually changing patterns of voxel to whole brain functional connectivity and their sudden transitions. We observed that functional connectivity gradients of the anterior hippocampus map onto connectivity gradients across the default mode network during these naturalistic stimuli. The presence of familiar cues in the news clips accentuates a stepwise transition across the boundary from the anterior to the posterior hippocampus. This functional transition is shifted in the posterior direction in the left hippocampus of individuals with MCI or AD. These findings shed new light on the functional integration of hippocampal connectivity gradients into large-scale cortical networks, how these adapt with memory context and how these change in the presence of neurodegenerative disease.