As Loyalists by definition, were they not satisfied with top-down British rule as it was in the Thirteen Colonies? This pro-democracy mindset would resound more with that of the rebels/patriots. So why be a Loyalist in the first place?
Being a Loyalist did not mean that person was completely in favor of all British policies, nor that they necessarily rejected all the developing ideologies that contributed to the American Revolution. It merely meant that they opposed separation from the British Empire, and that their future was better secured inside it rather than outside of it.
Check out Maya Jasanoff's Liberty's Exiles, which examines the 70,000 or so Loyalists which left (voluntarily or involuntarily, some were slaves) the US following the American Revolution. Many of them left for other parts of the British Empire and took a surprising amount of traditionally "American" values and ideologies with them, pushing for similar reforms in their new homes.