They do. My 2nd char only has the 1st matter board and I have only gray tabs on almost all the fields. Sometimes I get introduced to a new char when I go to a new planet but after that more gray tabs. Even some of the gray tabs from Naberius are on later planets.
The amount of new blue tabs that show up depends on how many matter boards you have. Some of the earlier tabs won't show up but will be replaced with the later tabs. For example my Main has up to matter board 9 and some characters like Tea and Patty or Klotho I get new blue tabs every time I've talked to them so far and they haven't gone gray yet.
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