The synchronisation itself (the "alignment") builds upen the open source "forced alignment" software "Aeneas" by Alberto Pettarin. We use this component to generate a time-based transcript (text fragments are linked to start -and end times in the video).
The method we use is based on the visual comparison of audio waves. Instead of using "speech-to-text" based on the original audio signal, we use "text-to-speech" to generate an audio version of the text proceedings. The wave form of this generated audio version is then visually compared with the wave form of the original audio. This makes the method almost language independent, as the pauses between sentences are more important for the synchronisation than the actual spoken word.
Before starting the alignment process we implemented many small steps that help us to find out which video matches which text fragment in the proceedings.