Here are my thoughts on Jyn's tonfa/baton. In order to take on armored Stormtroopers and Security Droids in hand-to-hand, close combat, the baton must be metallic, strong and lightweight. I would use that as the basic layer and think of metals such as steel or titanium in "our world". As a weapon, reliability is mandatory so the metal would need coatings to reduce oxidation (rust) and corrosion from heat, sand, salt water, etc. all of which are environments we see in the clips. Our world weapons are normally coated with a black oxide or "bluing" for clandestine operations such as might be expected of a spy, or use of stainless steel or chromium for a more flashy look. The tonfa seems to go the black oxide route which is a blue-black finish which seems consistent with a dark blue-gray-black look of the exterior. The surface of the exterior is "bumpy" this is for both ease of grip for the wielder and also as protrusions to concentrate the force onto small areas to the victim. In use black oxide wears down to bare metal so protected area between the bumps will be dark and the raised ends of the bumps will be lighter in some cases bare metal..
For the hand grip a non-slip grip is required. This is provided by a knurled surface with no coating. So this will be lighter than the other parts of the exterior even lighter than the "worn" ends of the bumps as this metal was never coated. The cross-hatch grooves of the knurling quickly collects dirt and grime. So dark grime is in the grooves and the top surface is lighter from all the "polishing'" from handing. This area gets the most wear.
The band which connects the handgrip to the main shaft and provide a pivot point is brighter than the shaft or the grip. There is no justification for this I can come up with other than just to provide visual interest.
For the extended tonfa the rules are different. Once it is deployed, stealth is less necessary. Coatings are not as necessary as the interior is normally sealed and protected in the collapsed state. In the video clips the interior is also shiny. My interpretation of this is that in a world of light-energy blasters and lightsabers, having a highly reflective surface to deflect those energies could be advantageous.
Also just so there is no confusion, the prop used on Kimmel's live segment is not the same as the weapon in the clips.
Attached are a series of screen captures of the tonfa in action. There are a number of still photographs but the colors are as questionable as fabric colors have been. They are helpful to recognize levels of contract and similarity to other "known" surfaces such as her sidearm which goes from the rear black coating to the shine of the barrel shroud.
EDIT Remove attached file as the PDF did not provide clear images. I will attempt to repost once I have corrected the issues.