The Okinawan Wonder site , amongst others catorgrises Matsubayashi Shorin Ryu as Tomari Te karate. It has also been said that the style is often 'confusingly' called shorin ryu.

For sure we train in tomari te kata within the style.

I am not qualified to really make any judgements and the advice of looking at Sensei McCarthys Koryu Uchinadi is certainly solid.
Jim Neeter