Or does it mean that contrary to Read Committed Isolation Level, uncommitted changes from a parallel transaction can affect the execution of an INSERT command?
This. Because you are keying off of an unique index that has independent isolation mechanics. Upon attempting to insert a row that will violate the unique constraint enforced by the index the system must wait to see whether the earlier transaction commits. If it doesn't, the insert proceeds. If it does, the conflict clause is evaluated - updating the now committed row (or just doing nothing if that option is specified.)