What I see here is that the one dollar is lost in translation.
Let's look at it as if no mistake was made at the beginning. $25 would need to be split between three people. Those people each paid $9 to the manager. If they each pay $8 dollars, then they would be one dollar short. Now, the manager has $2 left. He can't give it back to them because then it would be uneven. So, he gives the bellboy the two dollars. 9 x 3 = 27. 27 - 2 = 25.
Now, we can go back to the original situation. You have three more dollars used. 27 + 3 equals 30. All three men payed $10. The bellboy gave three back. 30 - 3 = 27. Then the bellboy kept two. 27 - 2 = 25. When you have it as one dollar missing, you are only using the wrong equations. $30 was paid overall. $5 was then given back, making $25. In what you said above, it simplifies to you doing 30 - 3 + 2 = not 30. Different equations had to be used. 30 - 3 - 2 = 25, the original spent.
There is no extra dollar, because the total spent is 25, not 30.