We investigate the interplay between post-translational folding and escape of two small single-domain proteins at the ribosomal exit tunnel by using Langevin dynamics with coarse-grained models. It is shown that at temperatures lower or near the temperature of the fastest folding, folding proceeds concomitantly with the escape process, resulting in vectorial folding and enhancement of foldability of nascent proteins. The concomitance between the two processes, however, deteriorates as temperature increases. Our folding simulations as well as free energy calculation by using umbrella sampling show that, at low temperatures, folding at the tunnel follows one or two specific pathways without kinetic traps. It is shown that the escape time can be mapped to a one-dimensional diffusion model with two different regimes for temperatures above and below the folding transition temperature. Attractive interactions between amino acids and attractive sites on the tunnel wall lead to a free energy barrier along the escape route of the protein. It is suggested that this barrier slows down the escape process and consequently promotes correct folding of the released nascent protein.