Dynamic surface effects in the isoscalar dipole modes of heavy nuclei are studied within a semiclassical model based on the solution of the Vlasov kinetic equation for finite Fermi systems with a moving surface. The isoscalar dipole strength function and the velocity field associated with the isoscalar dipole modes obtained in previous papers using the semiclassical model are considered in the dynamic-surface approximation, which takes into account only the part of the variation of the phase-space distribution function caused by the dynamic surface. It is found that the dynamic surface effects have an essential influence on the features of the isoscalar dipole modes. The isoscalar dipole strength function has a two-resonance structure already in the dynamic-surface approximation, and the centroid energies of both the low-energy resonance and the high-energy resonance are close to corresponding centroid energies of exact strength function. Calculations of the velocity field in the dynamic-surface approximation show the vortex character of the low-energy isoscalar dipole resonance and the compression character of the high-energy one, which are similar to the corresponding exact velocity fields.