The situation in Santo Domingo in 1788 was unclear. It was French in theory, one of the largest French colonies, but as the revolution in France was neither popular to Britain or Spain, the revolutionary government barely could have a presence in the island. This held for every other French colony.
As Spain begun to give refuge to French nobility, including former King Louis XVI, there were a strong movement to ask Spain to take control of Santo Domingo back. While Spain did not formally recognized the revolutionary government, Spain attempted not to confront the French so directly, but as Britain begun taking control of other French colonies Africa and the Caribbean, the Spanish hurried to Santo Domingo.
In June 1791, the Spanish took effective control of Santo Domingo and Port du Prince, without opposition by the British. This, among other issues in the Mediterranean and the Spanish-French border, lead the French revolutionary government to declare war to Spain.
France advanced over Barcelona in the winter to 1792. The French fought the war on land or near to the shore on Mediterranean waters, but the Spanish attempted to grab as much of French colonies as the British allowed. By spring 1792, Spain had freed Barcelona back and a first treaty was signed between Spain and revolutionary France. This recognized Spanish control over Santo Domingo. All other French colonies would return to France and some border adjustments were made on the European borders, mostly favoring France.
Spain would recognized property rights of French subjects in Santo Domingo. The Spanish government also promoted French refugees to go to Santo Domingo and to claim any unused land. However most of the former French nobles that migrated to the Americas chose Florida over Santo Domingo.
In 1797, a slave revolt started in western Santo Domingo. The Spanish put most of their resources to crush that rebellion. This lead many Frenchmen to move to Florida or to return to Europe. The rebellion were practically crushed by late 1799.
After the war against the USA, the Spanish were still hunting rebels in Santo Domingo, but must French institutions in the island had disappeared.