Let me step you through this, based upon fact.
If you have committed a crime, either a misdemeanor or a felony, and your fingerprints are taken, your information is entered into an FBI database. If you were a member of one of the U.S. Armed Forces or civil service and you applied for a security clearance, your fingerprints were taken as part of that process and entered into the FBI database.
When you register your name on an international flight information about you from that database can be appended into the flight manifest. The information does not prohibit you from leaving the host country, with the exception of a want or warrant that is extraditional in the host country. The U.S. and Canada share access to that database and other databases, and INTERPOL shares information as well. Prior to your arrival to a foreign country, that country's immigration service is aware of information that on that manifest and any information that was appended from the databases to the manifest.
There are a lot of variables that occur in the foreign country prior to the arrival of an international flight:
1) Ongoing investigations of travelers who may be involved in activity in the country of arrival, or of known investigations concerning certain crimes in the country of arrival to which a traveler may or may not be involved.
2) Evaluation of information that is included in the flight manifest.
3) Guidelines written by the country of arrival's government to determine how to admit or deny entry based upon several disqualifying and mitigating factors.
4) Evaluation of previous travel to that country.
4) An interview process at the port of entry (What is your purpose for travel, where will you be staying, etc.. as well as an evaluation of your demeanor during the process).
The "blacklist" being referred to is a result of information taking the flight's manifest and other country of arrival specific evaluation into account. DHS does have a list of suspected wrong doers who are subject to more scrutiny prior to boarding a flight, and immediately upon entering the country when a flight lands. Foreign countries may and do share a similar process.
It is not possible for a foreign country to know who is traveling to one of their ports until the flight manifest is received. Any special list being referred to is based upon information in the flight manifest and local country guidelines. The origination of the process of being placed on any list is the origination of booking a flight, cruise, whatever, and if there is a "blacklist" for DR, it is created by the DR based upon their evaluative processes. One cannot know the criteria set by a foreign country to approve or deny entry, because of the number of variables involved. The process is very fluid, but once you have been denied entry chances are very good you will continue to be denied.
Example: You could be a feloniously convicted drug traveler taking a cruise or traveling with a tour group and be admitted. You could be that same person traveling alone, and recent activity at the port of entry has resulted in arrests at that port that are similar in nature to your conviction, and you are denied entry.
Example: The flight manifest was not evaluated and you are admitted.
Example: A guideline in the foreign country states that no one will be admitted based upon a conviction of X and you are denied.
Example: You enter a foreign port and appear suspicious, nervous, dodgy at the entry interview...entry denied, even with nothing on a flight manifest.
Again, any special list is based upon, or originates from, flight manifests, country specific guidelines, and interviews at the port of entry.