Many manufactures make the claim "Will stick to glossy surfaces without sanding". The only primers that I use in this situation are from Zinsser or XIM. Zinsser's Cover Stain and 123 acrylic are both very good and XIM 400 series primers will stick very well. Both companies have primers that are tintable.
I never used the Valspar primer so I can't say if it will work or not.