My professor mentioned this briefly but did not elaborate further on the topic or did not explain it well. I mean, Jefferson was a founding father, what drove him to break the constitution so early after its ratification
This is a common misconception about Jefferson's views. Jefferson was not opposed to advancements in technology. Indeed he himself incorporated many new industrial technologies in his plantation at Monticello. What Jefferson was opposed to was the domination of the country through a commercial oligarchy, as had occurred in Britain. He also expressed concern about the environmental degradation reckless industrialism brought on. His position was more that the Industrial Revolution needed to be regulated by a democratic authority rather than that it needed to be rejected wholesale. Citation
Also, while Jefferson and Madison did debate about this, the Louisiana Purchase arguably was constitutional as Article II, Section 2 of the Constitution gives the President the power to orchestrate treaties with oversight from Congress.
Can you elaborate on him "breaking" the constitution? I'm confused.