The cameras on the rovers are not the same as the camera on your phone or a DSLR. Each camera has specific sensors for different wavelengths of light [0]. The images are really just the wavelength reflection intensity measurements (think of it like RAW images on a DSLR but for more than just RGB).
The colorization is done by taking several of these images for wavelengths and adding them together. For example blue is in the 450–495 nm wavelength, green 495–570 nm, and red 625–740 nm. The Mastcam on the curiosity rover is actually two cameras with various sensors for different wavelengths (including wavelengths outside the visual range). They can use these images to create color images. You take the 440 nm sensor and give each pixel a value between 0-255 and display that with more/less blue. Take the 525 nm or 550 nm sensor and make them green and the 675 nm sensor and make them red. When you combine these you get an image that looks pretty similar to what it would look if you were really there (It's called true color and false color [1]). This same process is used by satellites as well to measure and classify things on Earth from space. They way different surfaces reflect light in different wavelengths help scientists classify things on Earth and Mars and all over the solar system. (It's Okay to Be Smart on YouTube has a cool video about Infrared [2])
One of Curiosity's cameras has a Bayer Filter Array and practically shoots like a DSLR. You can download the (debayered) "raw" files which are simply 1408x1200x1 (channel, uint8) panes one under the other in RGB order. So basically an 8bit grayscale 1408x3600 image that you can open with GIMP in "raw image data (.data)" mode and fill in the data in the settings window.
But you are right that many times scientific missions will have monochrome CCDs with a filter wheel on top (Cassini, Galileo, Rosetta, Dawn to name a few).
