Pitcher Substitution

[StrikeDavis]

American Legion Baseball, between the top and bottom of the 5th, HT down 5-2.  VT has a player come off the bench and walk out to the mound.  From what I was told after the game, he was told he was going in to pitch the 6th inning earlier in the game by his coach but got the inning wrong (despite a functioning and accurate scoreboard in direct sight of the VT dugout) and headed out to the mound in the 5th.  He picked the ball up and stood on the back downslope of the mound while he waited for the catcher.  I asked the coach if it was a straight change.  He looks confused, so I pointed to the mound where his relief pitcher is waiting for the catcher.  He asks me if his relief pitcher standing on the mound constituted a substitution.  I told him that it did not, but if he threw a warmup pitch than it would have.  VT coach sends the starting pitcher back out to the mound and the relief pitcher goes back to the bench without throwing a pitch. While I was conversing with the VT coach, The 1B coach for the HT asked the BU if the player going to the mound like that was a substitution. BU gave him the same answer I gave the VT coach.  VT coaches are satisfied with the explanation and we move on without further incident.  HT ends up winning the game 6-5 after the relief pitcher that doesn't know what inning it is spent the 6th inning hanging curves and giving up 4 runs.  Speaking with some other umpires, I got some feedback that we should have considered it a substitution since the player came off the bench to the mound.  So would this scenario have constituted a substitution or not?      

[maven]

Under OBR, an unannounced substitute pitcher has entered the game when he "takes his place on the pitcher's plate." 5.10(j)/3.08(a)

So neither you nor the "other umpires" were correct: throwing a pitch is not it, nor is "standing on the mound."

That said, I would have handled it as you did. If the sub hasn't thrown a pitch, I probably won't see whether he has engaged the rubber, and thus allow him to be removed.