Context. The asymptotic giant branch (AGB) phase of evolution in low-and intermediate-mass stars is governed by poorly understood physical mechanisms, such as convection, mixing, dust production and mass loss, which play a crucial role on determining the internal structure and the evolution of these stars. The spectra of post-asymptotic giant branch (post-AGB) stars hold critical chemical fingerprints that serve as exquisite tracers of the evolution, nucleosynthesis, and dust production during the AGB phase. Aims. We aim to understand the variation of the surface chemistry that occurs during the AGB phase by analysing results from observations of single post-AGB stars in the Magellanic Clouds. We also aim at reconstruct dust formation processes, that are active in the circumstellar envelope of AGB stars, occurring towards the end of the AGB phase and during the subsequent course of evolution when contraction to the post-AGB has begun. Methods. We study likely single post-AGB sources in the Magellanic Clouds that exhibit a double-peaked (shell-type) spectral energy distribution (SED). We interpret their SED by comparing with results from radiative transfer calculations, to derive the luminosity and the dust content of the individual sources. Additionally, we compare the observationally derived stellar parameters and the photospheric chemical abundances of the target sample with results from stellar evolution modelling of AGB and post-AGB stars. This allows for the characterization of the individual sources in terms of initial mass and formation epoch of the progenitors. The theoretically derived dust mineralogy and optical depth is used to assess when dust formation ceases and determine the propagation velocity of the dust-gas system during the post-AGB evolution. Results. We find that amongst our target sample of 13 likely single post-AGB stars with shell-type SED, 8 objects are carbon stars descending from ∼ 1 − 2.5 M progenitors. 5 of the 13 objects are of lower mass, descending from M < 1 M stars. Based on the dust mineralogy, we find that these 5 stars are surrounded by silicate dust, and thus failed to become carbon stars. The dust optical depth and the luminosity of the stars are correlated, owing to the faster evolutionary time-scale brighter stars, which makes the dusty layer to be closer to the central object. From our detailed analysis of the SEDs, we deduce that the dust currently observed around post-AGB stars was released after the onset of the central star contraction and an increase in the effective temperature to ∼ 3500 − 4000 K.