Context. The European Space Agency's Gaia satellite was launched into orbit around L2 in December 2013. This ambitious mission has strict requirements on residual systematic errors resulting from instrumental corrections in order to meet a design goal of sub-10 microarcsecond astrometry. During the design and build phase of the science instruments, various critical calibrations were studied in detail to ensure that this goal could be met in orbit. In particular, it was determined that the video-chain offsets on the analogue side of the analogue-to-digital conversion electronics exhibited instabilities that could not be mitigated fully by modifications to the flight hardware. Aims: We provide a detailed description of the behaviour of the electronic offset levels on short (<1 ms) timescales, identifying various systematic effects that are known collectively as "offset non-uniformities". The effects manifest themselves as transient perturbations on the gross zero-point electronic offset level that is routinely monitored as part of the overall calibration process. Methods: Using in-orbit special calibration sequences along with simple parametric models, we show how the effects can be calibrated, and how these calibrations are applied to the science data. While the calibration part of the process is relatively straightforward, the application of the calibrations during science data processing requires a detailed on-ground reconstruction of the readout timing of each charge-coupled device (CCD) sample on each device in order to predict correctly the highly time-dependent nature of the corrections. Results: We demonstrate the effectiveness of our offset non-uniformity models in mitigating the effects in Gaia data. Conclusions: We demonstrate for all CCDs and operating instrument/modes on board Gaia that the video-chain noise-limited performance is recovered in the vast majority of science samples.