How new is the tank? Chaeto needs nutrients to grow; in a nutrient poor aquarium those ingredients may be hard for the plant to absorb. Do you have current readings for your phosphate or nitrate? What about the rest of your system - are you using a protein skimmer or phosban reactor?
Regarding the light itself, I can't speak much for your particular product. Yes, "PAR 38" bulbs will grow chaeto, but that name has gotten pretty vague in recent years. Personally I use an LED grow bulb for my fuge. And yes, when I first started the tank, it didn't do much for my chaeto ball. But after a year's break-in time, my chaeto is growing like mad and I'm harvesting half my growth monthly.
In fact, here: here's the exact bulb I've been using:
https://www.amazon.com/gp/product/B079NM682K/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1