It looks as if your text may originate from CPFilms (Solutia), a US company. It may therefore be helpful to have a look at some of their English-language material.

Patented processes for deep-dyeing and adding the toughest scratch resistant coating on the market are also incorporated into Llumar® performance film manufacture.
http://www.buildingdesign.co.uk/facil-group2/cp-films/

Color Dying
During the patented computer-controlled "deep dying process" the polymer matrix is penetrated by UV absorbers and/or colour pigments. In this way the films are directly tinted and not merely coated with colour, thus attaining the best possible colour stability and resistance to abrasion.
http://www.tintauto.com.my/technology.html

The above chart compares the performance of two common coloration techniques for the manufacturing of solar control window films - our deep-dyed polyester films versus color coating.
http://www.solutia.com/pdf/pf/ValueSeriesBulletin.pdf

Also, see this similar use of the terminology by another company in another field:
A patented deep-dyeing process is then used to impregnate the polymer matrix of PET film.
http://www.hospitalnetwork.com/product.mvc/Transparent-UV-Ab...