First, I understand that 3rd card isn't a T213-1; it's a -2, I lack the -1.
Ray Demmitt's transaction line says that on December 16, 1909 the New York Highlanders traded him and Joe Lake to the St. Louis Browns for Lou Criger.
Now... setting aside all of that print run stuff, two things. Thing one, it seems unlikely that American Litho could have printed Demmitt with St. Louis prior to mid December 1909. Thing 2, American Litho could have printed Demmitt cards with St. Louis on there at most any reasonable time thereafter... February, maybe wait until April to see if he's up... any time. They could have even still sent out New York cards for a few months until they got the change in.
This wasn't like a newspaper, where there's some token attempt at getting something correct. These guys were just printing insert cards for a tobacco company, I don't think they were too torn up about minor mistakes or shortcomings.