Conformally invariant scalar equation allows one to impose the Robin boundary condition at infinity in asymptotically-AdS spacetimes. In our work, we show how the dynamics of conformal cubic scalar field on the Schwarzschild-anti-de Sitter background depend on the black hole size and the choice of the boundary condition. We also discuss the work in progress regarding the charged black hole case. This is joint work with Maciej Maliborski.