I just fought and won my first battle with Dinos around 6-8 weeks ago, my tank was around 14 months old at the time.
I used my kids microscope to identify the Dinos as Ostreopsis, which go into the water column when lights are out.
My Phosphates bottomed out, so i dosed
Neophos twice a day at .022PPM (5ml) per dose.
I got a 36W UV sterilizer, which is a little over kill for my 60G display, and ran that for a full 72 hours.
I did a full blackout for the first 24 hours covering all sides and the top of the tank in cardboard, after the first 24 hours, i took the carboard off the top of the tank, and just ran blue and UV light from my tank light as i was afraid no light would stress out the coral and BTA which split during the blackout.
After 3 days of the UV Sterilizer running, the 24 hour total blackout and 48 hours of "hybrid blackout" I see no more Dinos.
After i noticed no more Dinos and took the cardboard off, left my refugium off, did a water change after 4 weeks instead of 2, and still dosed
Neophos, my UV sterilizer is now on for around 9 hours a night, which i plan on reducing to 6 hours.
I have noticed no more Dinos.
My advise would be to identify the type of Dinos you have, and check your phosphate levels, if they are at or near 0 then start dosing phosphates, and if you have the type of Dinos that go into the water column on a night time do a blackout, and if possible get a UV Sterilizer.
If you do get a UV sterilizer you will need 1 watt per 3 gallons of water, so a 15 gallon tank will need a 5W UV sterilizer. You also need to turn over the full tanks water volume every 20 minutes, for a 15 gallon tank you need the pump to do at least 45gph.