The quickCheck algorithm described in Section 9 of UAX #15, much like the normalization algorithm, does not change.

What the PRI background document is saying regarding the NFC_Quick_Check property is that if, instead of using the values of the NFC_Quick_Check property from the UCD, you are trying to compute the values yourself based on the decompositions (don’t do that!), you might get it wrong (indeed, the tools we use to derive those properties were getting it wrong until I fixed them).

Note of course that you still have to go through a proper normalizer when quickCheck says « Maybe », and if that normalizer is cleverly optimized, it may turn out to be too clever for its own good (this is the case of the ICU normalizer and the ICU4X normalizer).