What is the logic for mapping the FB and RB depth chart to the 3 backs in the wishbone formation?
If I run this formation the first two plays of the game (which I assume means no one is tired yet), I get different players, including the 3rd string RB.

on the depth chart screen you can click "view formation" to see where they line up. But the runs out of wishbone are set up, so either RB may get the carry on a given play.

I run the same play the first 5 plays of the game.

On the second play - my third string RB lines up in the position called wing back in view formation
On the fifth play - my third string RB lines up in the position called running back in view formation

Something similar to this has happened in at least 3 consecutive games.

Are players already tired and being substituted for on the second play of the game?

my guess is you are using running back by committee