what you are probably seeing is the AIs singular examples of mastery
ie. an AI faction focused on a single tech tree, so they have good ships or better gunpowder units, etc.
when in reality they don't have much else
I personally prefer them to get the benefits at the same rate as me, since there is only so much fun to be had crushing untrained basic armies over and over again and assaulting small forts.
the trainer just helps speed it along a bit
^This
When I conquered *insert name of island where Shimazu clan starts here* with the Mori ~1560 they already had the the roads at it's maximum level while I had them at the previous level, but they didn't have No-Dachi Dojos or Drydocks.