Hello,
I've been working in the colorimetric world for 15 years and this device is a very classic one.
First of all, it is NOT a spectrophotometer. It is a colorimeter.
The principle is the use of 3 filters to obtain a physical space representing the color. But, this has a lots of inherent limitations. These filters are in fact the standard CIE observer curves (the 1931 2° one). The x one has two humps, related to a weird property of the human vision. All measurement devices use CIE coordinates, which can be XYZ, Lab, LCh... RGB, or CMY(K) are NEVER used in physical measurements. They are useless because they are device related. The link between CIE coordinates and device related coordinates is done using tables (or some formula in very, very specific cases). This is the goal of ICC profiles for example. RGB (CMY) space are not physical and not defined.
All colorimeters use the very principle of filters, but they are NOT RGB or CMY stuff. There is a R,G,B space in CIE definitions using r,g,b observer curves. But this is NOT related in any way to the usual RGB space used in the computer world. RGB or CMY(K) are the worst spaces to work with when you manipulate colors seriously.
The other limitation of a colorimeter is that they are stuck to a given illuminant (or light), often D65 or D50. And there is no way to convert a CIE coordinate in one illuminant to an other. There are some techniques (like the Bradford transform), but they are only crude approximations. The only way to get real colorimetric measurements is from a spectrophotometer. From that point, you can compute any CIE coordinates you want.
Colorimetry is a very rich science subject and it is a shame that it very under-used in the computer world. For example, Adobe software have very archaic color management even in 2016 and there is no way to print accurate colors with usual software, even though everything is available to do so !
Jerome.