You're mainly taking offense with the lack of a citation, I think, but I might be able to at least explain the timeframe mentioned here. I'm neither a doctor nor working in this field, so take everything with a grain of salt:

The incubation period is usually five days or more, while patients can already be infectious two days before symptoms show. That means there is a window of opportunity of 2-3 days to find contacts of the current case and put them into quarantine before they start infecting even more people.

Where the percentage comes from, I do not know but I would assume that it is meant to push the number of new infections per case (R = reproduction number) to 1 or even better well below it (R < 1 means it would eventually fizzle out). Super sketchy math: if the reproduction number is ~2.5 and you trace and quarantine 90% of the contacts (1 - 0.9) * 2.5 ~= 0.25 new cases will slip through. They might be aiming at such a high number to compensate for other cases where no tracing is done (e.g. because it was not known that the patient was Covid-19 positive) to keep the overall reproduction number low.

Once again - I am not a professional and just offering some thoughts about the problem (and happy to be corrected / to learn more).