Numerical simulations of double-barred galaxies predict the build-up of different structural components (e.g. bulges, inner discs) in the central regions of disc galaxies. In those simulations, inner bars have a prominent role in the internal secular evolution of their host galaxies. The development of bulges and inner discs is, however, poorly understood observationally due to the small number of studies focusing on the stellar populations of these systems. In order to provide constraints on the relevant processes inducing the creation of these components in the presence of inner bars, we have carried out a detailed kinematical and stellar population analysis in a sample of four double-barred galaxies, ranging from SB0 to SBb, observed with integral-field spectroscopy. We find that the inner bars present distinct stellar population properties, being younger and more metal-rich than the surrounding bulges and outer bars. While we detect signatures of gas inflow through the inner bars, we find no evidence of associated star-forming regions or newly formed structures around them. This result suggests that, regardless of their formation scenario, at present these inner bars are playing a moderate or even a minor role in the morphological evolution of this sample of double-barred galaxies.