On a curved surface, epithelial cells can adapt to geometric constraints by tilting and by exchanging their neighbors from apical to basal sides, known as an apicobasal T1 (AB-T1) transition. The relationship between cell tilt, AB-T1 transitions, and tissue curvature still lacks a unified understanding. Here, we propose a general framework for cell packing in curved environments and explain the formation of AB-T1 transitions under different conditions. We find that steep curvature gradients can lead to cell tilting and induce AB-T1 transitions. Conversely, large curvature anisotropy can drive AB-T1 transitions by hydrostatic pressure. The two mechanisms compete to determine the impact of tissue geometry and mechanics on optimized cell rearrangements in 3D.