Hollow vesicular tissues of various sizes and shapes arise in biological organs such as ears, guts, hearts, brains and even entire organisms. Regulating their size and shape is crucial for their function. Although chemical signaling has been thought to play a role in the regulation of cellular processes that feed into larger scales, it is increasingly recognized that mechanical forces are involved in the modulation of size and shape at larger length scales. Motivated by a variety of examples of tissue cyst formation and size control that show simultaneous growth and size oscillations, we create a minimal theoretical framework for the growth and dynamics of a soft, fluid-permeable, spherical shell. We show that these shells can relieve internal pressure by bursting intermittently, shrinking and re-growing, providing a simple mechanism by which hydraulically gated oscillations can regulate size. To test our theory, we develop an in vitro experimental set-up to monitor the growth and oscillations of a hollow tissue spheroid growing freely or when confined. A simple generalization of our theory to account for irreversible deformations allows us to explain the time scales and the amplitudes of oscillations in terms of the geometry and mechanical properties of the tissue shells. Taken together, our theory and experimental observations show how soft hydraulics can regulate the size of growing tissue shells.