Lets just get one thing straight. The tuner (ATU) doesn't do anything to the antenna.
It "matches" the antenna to the frequency which has been tuned on the T/R.
Dual HF systems have a single antenna (older (and possibly newer) 747 excluded which has separate antennas on each wing tip) with dual ATU's. Each ATU will be tuned to the frequency selected on its respective T/R and crew can alternatively talk on either HF without a retune required.
An ATU is basically a box containing (big) inductors and capacitors and a VSWR bridge. The tone heard during the tuning cycle is (as has been said) a low power modulated RF which the ATU uses to adjust inductance and capacitance via the bridge output until it is nul and the total ATU/antenna impedance is (usually) 50 ohms. These ATU's can be mechanical or digital but the basic theory is the same.