Fig. A.1: ttv_pla1_2.pdf TTV amplitudes obtained for TOI-396 b (black markers) and TOI-396 c (red markers). This is a superposition of the first two panels of Figure 4 in the paper emphasising the anti-correlation pattern. Fig. A.2: lcGLS*.pdf First column: Generalised Lomb-Scargle periodograms of TESS Sector 3 (lcGLS_3.pdf), 4 (lcGLS_4RawFluxrm.pdf), 30 (lcGLS_30RawFlux.pdf), and 31 (lcGLS_31RawFlux.pdf) raw photometry. Second column: Generalised Lomb-Scargle periodograms of the residuals (lcGLSRaw_3noSine.pdf, lcGLSRaw_4noSinerm.pdf, lcGLSRaw_30noSine.pdf, lcGLSRaw_31noSine.pdf) after removing the best fitting sinusoidal signals at the most significant frequency identified in the periodograms of the corresponding TESS time series. The long dashed red line marks the FAP at 0.1\%. Significant peaks are detected in the 6---8 day range, which we attribute to the presence of active regions co-rotating with the star.