Can Perspex or Acrylic Sheet be tinted

The simplest answer to that question is that applying film (solar, safety/security or decorative) to Perspex, Acrylic Sheet, or other 'plastic' panels is not recommended.

Perspex and other acrylic/plastic sheeting constantly release gas during their lifespan, when film is applied, then bubbles usually appear within a year, and they get progressively worse over time.

Also there is a reaction between the perspex and the films adhesive that makes it very 'grabby', and almost impossible to position the film correctly once it is applied to the surface. How much the film grabs depends on the brand and type of film, and the type of acrylic/plastic sheet.

So initially the film is very difficult to install, and then it bubbles within a relatively short period of time.

Unfortunately the options are limited to replacing the clear perspex with tinted perspex, or with glass, and then tinting that. The only other option to reduce heat is to hang shade-cloth outside the windows in summer, and remove it during winter.

If you are seeking total block-out privacy, then it is probably simpler and easier to just paint the inside surface of the perspex/plastic window.