Dynamic Hubbard models are extensions of the conventional Hubbard model that take into account the fact that atomic orbitals expand upon double occupancy. These models give rise to superconductivity driven by lowering of kinetic energy when the electronic energy band is almost full, with higher transition temperatures resulting when the ions are negatively charged. It is shown here that systems described by dynamic Hubbard models have a tendency to expel negative charge from their interior to the surface, and they have a tendency to develop charge inhomogeneity in the bulk. These tendencies are largest in the parameter regime where the models give rise to highest superconducting transition temperatures. We propose this physics as an explanation for the charge inhomogeneity, negatively charged grain boundaries and negatively charged vortices observed in high temperature superconductors. Below the superconducting transition temperature the models considered here describe a negatively charged superfluid and positively charged quasiparticles, unlike the situation in conventional BCS superconductors where quasiparticles are charge neutral on average. We examine the temperature dependence of the superfluid and quasiparticle charges and conclude that spontaneous electric fields should be observable in the interior and in the vicinity of superconducting materials described by these models at sufficiently low temperatures. We furthermore suggest that the dynamics of the negatively charged superfluid and positively charged quasiparticles in dynamic Hubbard models can provide an explanation for the Meissner effect observed in those superconducting materials that are not described by conventional BCS-London theory.