I think a video might explain better how a tamper does its job. A stoneblower effectively is a tamper with the extra ability to add more ballast in a controlled manner.
https://youtu.be/lQg1U5FxyS0Paul
It is not clear from the video, but the tamper is also lifting the track as well as squashing the ballast. As a student in the 1970's I worked on tamper development including the development of vibration to stablise the track after tamping (which was first used to allow track to be opened at line speed after blockades such as at Crewe) and the stoneblower development project.
The problem with conventional tampers is the track subsides back to its old profile. Most of this happens in the first few load cycles. Broadly the first load does as much damage as the next ten and the following 100 cycles.
Dynamic track stabilisers allow allow the track to be overlifted and then knocked back to the right profile before opening to traffic.
Stoneblowers work by blowing additional ballast under the sleepers with compressed air. It actually uses smaller sized stone otherwise it wouldn't get down the inside of the tines of the tamper.