That they do not clash with the Malaysians may be because the Malaysians chose not to pursue the matter?
Malaysia has no claim on any part of Thailand as any potential problems were averted following the 1909 Bangkok agreement signed between Britain and Siam, which settled the matter of Siamese claims on a number of states in then Malaya and drew the present Thai/Malaysian land border. There has in the past been disagreements on the sea boundary on the west coast leading to fishing boats being detained.
The Brits made a similiar deal with the Dutch over the Riau islands, which was part of the Johore - Riau empire, as a result the Riau islands are part of Indonesia. Though a lot of problems facing the world today in places like the Middle East and the Indian sub-continent are a result of artificial borders created by colonial powers for their interests, more often than not against the wishes of the locals, Malaysia is extremely lucky in that it's present day borders are have not resulted in any majors problems with it's neighbours.
2. The Majority of people in Pattini, Yala and Narathiwat are Thai Muslims … not Malay Muslims.
On the Malaysian side of the border, there are quite a few Malaysian Thai Muslims or people of mix parentage, who speak both languages and have relatives on both sides of the border. When I was in Phuket for the first time, I was suprised at the number of Thai Muslims who spoke Malay. I'm not sure if they were originaly from there or from provinces on the Thai mainland bordering Malaysia.