You can't adjust the saturation of that color to make it red, just a lighter shade of pink. There are pink colors that are closer to red than to purple, but pink is a different part of the color space than red is.
If you see the shade in that link as red or purple, then you're living in a hell of having no rational basis by which to talk about color, or possibly color-blind.
Up until the last few decades, English speakers would not consider the color in your link to be “pink”. “Pink” was another word for “light red” (not the name of a hue), named after a flower that looks something like https://www.stauden-stade.de/img/artikel/full/823.jpg
“Hot pink” is a creation of the fashion industry / marketers from the 1980s (or maybe 70s?).
If you want to be unambiguous, you should call the hue of your link purplish red or similar. You could also use a word like fuchsia (named after a different flower) or magenta (a purplish red ink used in 4-color CMYK printing).
This is pink: https://static1.squarespace.com/static/53cdd3f3e4b09b69bef6e...
You can't adjust the saturation of that color to make it red, just a lighter shade of pink. There are pink colors that are closer to red than to purple, but pink is a different part of the color space than red is.
If you see the shade in that link as red or purple, then you're living in a hell of having no rational basis by which to talk about color, or possibly color-blind.