That's not exactly the case. A citizen of a particular country, on voluntary travel, wishing to reenter their own country, cannot be denied entry.
Being officially deported from another country and returned home is governed by international convention. The steps usually involve notifying the destination country of who is being deported, why and when they will be returning. Many countries routinely deport and accept deportees without much fuss, if the deportation is not of a criminal nature. For other countries, Somalia, Miramar, most of the middle east, China, Russia etc. it is not usually a straight forward nor expedient affair.
Quickie deportations between amicable countries usually have a legal framework in place to facilitate the process. Generally, you can't drop kick someone out of one country to have them show up announced in another country, even if they are citizens of that country. Govt's always want to know who's coming and why...
Of course they have to notify the officials of said country of the deportees. I am not saying that they
are just going to drop kick them. Countries accept deportees(citizens) of criminal nature too.
The US deports criminals (Hispanics and other nationalities) on a monthly basis back to their
countries of origin. In the same way that the DR has and does deport criminals who've been hiding in the country back to their country.