Yes, you can be fined if you overstay your tourist visa, but the amount you pay depends on the amount of time you have spent in the country after your visa has expired. Below is a list of dates, and the corresponding fines for overstaying your tourist visa.
From 15 days to 3 months RD$ 300.00
From 3 months to 9 months RD$ 500.00
From 9 months to one year RD$ 2,000.00
From 1 year to 1 year and 6months RD$ 3,500.00
From 1 year and 6 months to 2 years RD$ 4,500.00
From 2 years to 2 years and 6 months RD$ 6,000.00
From 2 years and 6 months to 3 years RD$ 8,000.00
From 3 years to 5 years RD$ 12,000.00
From 5 years on RD$ 15,000.00