I don't think 'appe' and 'appUppa' has anything to do with matrilineal bond between Tuluvas and Malayalis. Since the word 'abbe' is also observed in literary Kannada (mostly Jain) and in the personal names of many Kannada Jain queens, that shows Jain influence in Kannada, Tulu and Malayala regions. Since Tulu region was under Jain rulers until 20th century, 'appe' probaby became a common term. Whereas, in Kannada region by 12th century all Jain ruling classes have vanished thus the elite word 'abbe' didn't become part of common parlance. I don't think there were any Jain rulers in Kerala region (not sure of the Tamil kings of the past), however, the influence could have been there as merchant classes generally patronized Jinaism.