The U.S has not exported democracy and the cementing of a democratic process, it has simply sought to create an American sphere of influence for its own benefit. As have all other world powers before them. This is easily seen by the character of the many nations that the U.S has either propped up, allied with or had close ties with over the last century. You dont have to look far to see this with Saudi Arabia, or the rightwing S.American dictatorships of the 70's and on, and on, and on.....
This is no different than what Britain/France did in their imperial height in regard to their own interests. In the scope of worldwide interventions when the U.S has worked with other nations, usually the result and goal has been the implementation of a semi-democratic order such as the previous wars in Iraq/Afghanistan (Though many conspiracy theorists would argue our reasons).
I also dont believe the U.S has created a Democratic world order. That is not to take anything away from what the U.S has done in terms of WW2 and its role since as world police officer. I see most of a democratic world order coming out of the independence of previous colonial nations from their respective colonial powers.. Britain/France/Netherlands/Spain/Russia/Portugal. Just the independence movement from Britain and France brought Democracy to almost all of Africa, huge parts of Asia including China (Which didnt pan out too well).
If there is a democratic world order then I see it as a result of the restoration of independence to previous colonial states that has allowed for this. Obviously the U.S was a large proponent of this but the U.S wasn't the reason there is one.
As to Puerto Rico as an example, the U.S history on exporting democracy does not stand up... The Cointelpro program was directly aimed by the FBI at distorting, infiltrating, discrediting and disrupting political independence movements within Puerto Rico. Puerto Rico is a territory under the sovereignty of the federal government, though Puerto Rican citizens have had U.S citizenship since 1917 they have no representation and have no vote on a federal level. This is not a portent of Democracy.
And lastly, i dont want to have a "school house argument"... I simply want to be accurate, the U.S is not a democracy, the word has been warped over the years and no longer has the same meaning when used by the vast majority that it has previously. The electoral college and large issues within the U.S electoral system can result in severe minority rule (Though there is a small chance of this it has happened twice before, once a small minority in 2000 and second Andrew Jackson in 1828 who won with a small minority) which wouldn't be possible in a true Democracy. Im not trying to be pedantic, I think its important to understand the difference's and some of the disparity between what people think they have and what they actually have.
Apologies, didnt intend for this post to be so long