FWIW, the correct league level stats seem to show up in the table. However, sometimes the level does not appear next to the player’s name in the “Name” field. Of course I don’t have an example to give at the moment…
Edit: odd example found: Ottoneu Fantasy Baseball - playercard - Rock and Fire - LT Titans ⚂ - Jared Young
Jared Young’s stats are a combination of AAA and A from this year, but his player’s name in the stat tables do not indicate a current minor league level. At a glance, it appears he is on the Mets major league club.