Recently, a population of compact main sequence (MS) galaxies exhibiting
starburst-like properties have been identified in the GOODS-ALMA blind survey
at 1.1mm. Several evolution scenarios were proposed to explain their particular
physical properties (e.g., compact size, low gas content, short depletion
time). In this work, we aim at studying the star formation history (SFH) of the
GOODS-ALMA galaxies to understand if the so-called ``starburst (SB) in the MS''
galaxies exhibit a different star formation activity over the last Gyr compared
to MS galaxies that could explain their specificity. We use the CIGALE SED
modelling code to which we add non-parametric SFHs. To compare quantitatively
the recent SFH of the galaxies, we define a parameter, the star formation rate
(SFR) gradient that provides the angle showing the direction that a galaxy has
followed in the SFR vs stellar mass plane over a given period. We show that
``SB in the MS'' have positive or weak negative gradients over the last 100,
300, and 1000 Myr, at odds with a scenario where these galaxies would be
transitioning from the SB region at the end of a strong starburst phase. Normal
GOODS-ALMA galaxies and ``SB in the MS'' have the same SFR gradients
distributions meaning that they have similar recent SFH, despite their
different properties (compactness, low depletion time). The ``SBs in the MS''
manage to maintain a star-formation activity allowing them to stay within the
MS. This points toward a diversity of galaxies within a complex MS.