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It's provided by OpenTripPlanner, the public transport data I managed to find around 2-3 years old, so I doubt it is very accurate. The usual google maps / citymapper and other routing services doesn't provide a way to generate the public transport isochrone or is too expensive/restricted
not sure if you found this, might be of some use to you https://github.com/yinshanyang/singapore-gtfs/
The source code is here, it might be a bit messy haha. There is no algorithm essentially, I used a bunch of open source software to do all the work. OpenTripPlanner for the public transport isochrones, MapBox Isochrone API for driving isochrone, and turf.js to calculate polygon intersections.