The points are tied to the class. (And any jobs associated with the class)

For example, if you put 30 points into MND for Conjurer, you will have 30 points in MND as White Mage.

For Arcanist, if you put 30 points into INT, you will have 30 points in INT for Summoner, and 30 points in INT as a Scholar as well. (Due to this, you might want to carry around some reset stones (Keeper's Hymn) if you plan on playing Summoner and Scholar. You can get them from your Grand Company for 250 seals each)