You moved the player at the right time. You can't move them at the end of the round, because if you've just started a new round, your tables would be unbalanced for all that time and it would be unfair on the smaller table. If you are going to move a player to balance the tables, it is best to keep the player's relative position the same. (eg. if you need a big blind, move the BB from the other table) TD won't do this for you unless you set the dealer buttons before table balancing.
There is a check box for final table seating, (not sure whether it's auto checked or not), TD will then randomize the final table for you, so the dealer button will be set at seat 1, but with players' seat positions changing it is, in effect, ranomized.
If you have time, try some mock tourneys to see how the software works, so that you know how things will be done and you can explain to your players what will happen, in advance.