Segaretro has a list of early games that screwed up TMSS support, and the Japanese version of Phantasy Star II is one of them:
http://segaretro.org/TradeMark_Security_System
That said, if putting the console in Japanese region mode fixes the issue, it could be more complex than just a TMSS problem.
The other TMSS-breaking carts from Sega (as opposed to unlicensed games like Onslaught) listed at Segaretro are all Japanese releases of launch or launch-ish titles, namely:
Alex Kidd
Altered Beast
Osomatsu-Kun
Space Harrier II
Super Daisenryaku
Super Thunder Blade
I wonder how many of those would work on a Model 2 or Nomad in JP mode?