Applying paint to a drywall ceiling after knockdown texture is applied

[Ken scv]

I am a DIY homeowner. Last week I had the popcorn on my drywall ceilings in my 50-year old southern California home removed, then the ceilings were refinished with a knockdown texture. I am now ready to paint but a family member recommended a product to stop bleed-through along the drywall joints. I thought my purchase of Valspar color-changing ceiling paint that includes primer to be rolled on my ceiling would suffice. Yet I am wondering if I should first apply a separate primer before applying the ceiling paint. Does anyone have any recommendations/advice?