Vacuum fluctuations can be engineered using optical cavities, resonators, and surface-polaritonic modes, but extending such control deep inside a material remains challenging.Here we show that the vacuum field inside a hyperbolic material can be reshaped by a much thinner overlayer with opposite hyperbolicity.This effect requires overlap between the hyperbolic bands of the two materials and modifies the coupling between the vacuum field and matter excitations within the bottom material, without changing its intrinsic dielectric properties. As an application, we use Eliashberg theory to study a two-dimensional superconducting layer inside the bottom material, showing that the overlayer can remotely change its critical temperature.Our results may shed light on recent experiments reporting changes in superconductivity arising from a frequency-matched hyperbolic overlayer, and suggest an on-chip route to long-range control of matter excitations and collective material properties.