Electric field-induced polarization switching underpins most functional applications of ferroelectric materials in information technology, materials science and optoelectronics. Recently, much attention has been focused on the switching of individual domains using scanning probe microscopy. The classical picture of tip-induced switching, including formation of cylindrical domains with size, is largely determined by the field distribution and domain wall motion kinetics. The polarization screening is recognized as a necessary precondition to the stability of ferroelectric phase; however, screening processes are generally considered to be uniformly efficient and not leading to changes in switching behaviour. Here we demonstrate that single-point tip-induced polarization switching can give rise to a surprisingly broad range of domain morphologies, including radial and angular instabilities. These behaviours are traced to the surface screening charge dynamics, which in some cases can even give rise to anomalous switching against the electric field (ionic field effect).