A pop-up rod on a the FO's control column on a DC-9 that shows the Mach trim position. (YouTube)
Regarding the title, I'm not sure if it's just some or all jetliners (I tried to research it). On the DC-9 family and 737NG, it is stated clearly in the FCOMs that the Mach trim moves the elevator to counter the Mach tuck. On the 737 the system starts operating above Mach 0.615 (See FCOM 9.20). And below is part of the text from the MD-80 FCOM:
Operating on a Mach schedule, the Mach trim compensator pulls the First Officer’s control column aft as Mach number increases. As the control column moves aft, an indicator rod on the left side of the First Officer’s control column extends, giving visual indication of Mach trim operation.
Why don't the mentioned Mach trimmers use the stabilizer? I always thought the stabilizer had more fine control, not to mention the drag penalty of an offset elevator. There must be a reason for moving the control column aft and not just trim the stabilizer.
I checked these posts where Mach tuck was discussed: