The words 'aggressive move' do not appear in the rule as written, so my humble suggestion is to try to get it out of your thought process, because the word 'immediately' DOES appear.
As far as putting your team in the best position to score, there's zero upside to hanging out off 3B for '3-5 seconds' when the pitcher has the ball IN THE CIRCLE. With no other runners behind her - and no chance to score without an errant throw - there's all cost and no benefit.
Yes, the exception is part of the rule as explained by MTR, but the wiser course of action is to play to the rule as opposed to playing to the exception. It's a tough call, but as you described the situation, it sounds like the umpire was correct by the letter of the law. I teach aggressive base-running, too, but once the pitcher has the ball in the circle, if you stop the player, then she's got to immediately get back to the previous base.
Our runners can attempt to bait the opposing catcher into a throw, but not a pitcher with the ball in the circle.