Here is what the minister said in the OP: "Jesús (Chú) Vásquez, the named Minister of Interior & Police in the upcoming Luis Abinader presidency, says the next government will apply the General Migration Law 285-04. He said the law was passed when he presided the Senate in 2004. “Nothing needs to be invented. Just apply the law,” he says. He says Juan Manuel Rosario, who consulted on the law back then, would work with him as Deputy Minister of Interior & Police, responsible for the migratory matters."
Here is a link to current DR immigration law. You will see there is no mention of overstay fees anywhere since those fees are outside the law:
It is impossible to post a link in the law about overstay fees because they are not part of DR law.
Hence paying them does not change anything with regard to DR immigration laws.
DR immigration law was updated in 2004 by the PRM just before they lost power. The PLD worked around the law. What a surprise.