We extend our previous work on the age-chemical abundance structure of the Galactic outer disc to the inner disc (4 < r < 8 kpc) based on the SDSS/APOGEE survey. Different from the outer disc, the inner disc stars exhibit a clear bimodal distribution in the [Mg/Fe]-[Fe/H] plane. While a number of scenarios have been proposed in the literature, it remains challenging to recover this bimodal distribution with theoretical models. To this end, we present a chemical evolution model embedding a complex multi-phase inner disc formation scenario that matches the observed bimodal [Mg/Fe]-[Fe/H] distribution. In this scenario, the formation of the inner disc is dominated by two main starburst episodes 6 Gyr apart with secular, low-level star formation activity in between. In our model, the first starburst occurs at early cosmic times (t ~1 Gyr) and the second one 6 Gyr later at a cosmic time of t ~ 7 Gyr. Both these starburst episodes are associated with gas accretion events in our model, and are quenched rapidly. The first starburst leads to the formation of the high-α sequence, and the second starburst leads to the formation of the metal-poor low-α sequence. The metal-rich low-α stars, instead, form during the secular evolution phase between the two bursts. Our model shows that the α-dichotomy originates from the rapid suppression of star formation after the first starburst. The two starburst episodes are likely to be responsible for the formation of the geometric thick disc (z > 1 kpc), with the old inner thick disc and the young outer thick disc forming during the first and the second starbursts, respectively.