When importing records using the update or fill option, phone numbers are not imported unless at least one phone record already exists. Confirmed on Sandbox 2.1.
John Doe (287) has two phone numbers defined.
Jane Doe (291) has no phone numbers defined.
Import attached file (use Phone Import - Update map). John Doe's phone numbers will be updated and a third phone added. No data is imported for Jane Doe's record (because she did not have a preexisting phone record).