we perform all experiments at the plateau edges, where co-tunneling randomizes the electron spin [@Smith2005].

All time-resolved measurements are performed by using superconducting single-photon detectors. The overall timing resolution for the $g^{(2)}$-measurements is $\text{IRF}\simeq35\ \text{ps}$ (full width at half maximum). Optical measurements are carried out at $4.2\ \text{K}$ in a helium bath cryostat. Resonant excitation of the QDs is performed with a narrow-bandwidth ($\sim1\ \text{MHz}$) tunable diode laser (Toptica DLpro), which is additionally filtered with a home-built grating setup in order to remove any background from the gain medium of the laser. Resonance fluorescence of individual QDs is measured by suppressing the reflected laser light with a cross-polarization technique.

Modeling the Magnetic Field Dispersion
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![image](fig_s2e){width="1.8\columnwidth"}

The radiative Auger emission appears on resonantly exciting the trion. Fig. \[fig:mechanismFull\](a) shows a comparison of the emission spectrum from a neutral exciton and a trion. The emission spectrum of the neutral exciton ($X^0$) only shows phonon-related features. A radiative Auger emission is impossible for the $X^0$ due to the absence of an Auger electron.

The final states after the optical recombination of the trion are single-particle states. Therefore, the separations between the different emission lines are precise single-particle energies. Shown in Fig. \[fig:mechanismFull\](b,c) 