Aims. We aim to investigate the connection between star formation histories (SFHs) and the inner dark matter density profiles of simulated galaxies. In particular, we tested whether the burstiness and temporal distribution of star formation influence the formation of cored versus cuspy dark matter profiles. Methods. We homogeneously analysed simulated galaxies from the NIHAO and FIRE-2 projects. For each galaxy, we derived dark matter density profiles and measured the logarithmic slope in the inner region of the dark matter halo (1─2% of Rvir). To characterise the star formation burstiness, we introduced a criterion based on comparing the star formation rate (SFR) averaged over two distinct timescales. We further quantified the temporal concentration of SFHs by computing the ratio of stellar mass formed after versus before the epoch of re-ionisation at redshift z ∼ 6.5, expressed as M★, post/M★, pre. Results. A homogeneous analysis reveals that inner slope versus stellar-to-halo mass ratio trends for NIHAO and FIRE-2 galaxies are in much better agreement than what has been reported in previous works. The burstiness and post-to-pre re-ionisation stellar mass ratio explain the scatter in the inner slope versus stellar-to-halo mass ratio relation, revealing that galaxies with a burstiness above average and a more extended SFH are more efficient at developing cored dark matter profiles. In contrast, galaxies with smoother SFHs and an earlier stellar mass assembly time tend to maintain cuspier dark matter profiles. We present an analytic expression that improves predictions for the inner slope using M★, post/M★, pre, which reduces the mean square error in both simulation suites relative to previous formulations based solely on the stellar-to-halo mass ratio.