Visa curtailment date

How does the home office decide on the date of curtailment in case of early completion of studies?

This is quoted from a university site:
"within four months of the date you receive this email notification because we cannot predict when the UKVI curtailment team will take action".

Does that mean its from the date the university report is made to the home office? They add 4 months from the date the report was made?

See the guidance on Cancellation of entry clearance and permission casework guidance, page 50:

Cancelling permission: student or child student
..
If you are cancelling a student’s permission because they have successfully completed their course early, you should normally cancel permission so that the individual is left with the same wrap-up period of permission after the new course end date as the period they were originally granted based on their original course end date. For example, if a student was originally granted permission with a wrap-up period that would have expired 4 months after the end date of their studies, you should normally cancel their permission such that they have 4 months permission remaining after the new end date of their studies.

https://www.gov.uk/government/publicati ... ent-action

The visa will be curtailed (now called cancelled) to the new end date of studies + 4 months.