Did Jefferson stay true to the values of "Jeffersonian Democracy" while he was president?
For the most part, Jefferson did stay true to the values of Jeffersonian democracy when he was president. He did this in ways that were symbolic and in ways that were more substantive. Symbolically, for example, Jefferson did not like ceremony and other shows of power in his administration. He had a simple inauguration ceremony. He rode a horse around town rather than being pulled in a carriage. He reduced the amount of protocol at White House dinners. In all of these ways, he was following his egalitarian instincts.
In more substantive ways, Jefferson tried to reduce the size of government. He repealed, for example, the whiskey tax and other excise taxes. He also cut back on military spending since he thought that a militia was better because it was less susceptible to being used to help the government tyrannize the people. Finally, Jefferson bought the Lousiana Purchase. By buying so much land, he was making it more possible for small farmers to own their own property. This was very much in line with his principles.
Of course, Jefferson was not 100% pure. The Louisiana Purchase itself was disliked by some Jeffersonians because there was nothing in the Consitution that said the president could do such a thing. Jefferson also did not try to destroy Hamiltonian initiatives such as the Bank of the United States. In ways such as this, Jefferson was not a dogmatic Jeffersonian.