It is not a problem at all. We can use the 861 or 321 movement as the example. The reset hammer for the minutes and seconds is under constant tension. It is held in place by a post which has a spring action against it. When the reset pusher is pressed that post is moved to the side and allows the hammer to be released and act against the heart shaped cams of the chronograph wheels.
Once the reset pusher has been pressed that hammer stays in that position until the chronograph has been re-started.
If the chronograph complication has already been reset then pressing the reset pusher will only move the small post back and forth.
The post is circled below. The movement used for the example here is an Omega 321.
The hour recorder is reset via a different hammer on the dial side of the movement, which will act against the heart cam of that wheel when the pusher is pressed, however there is no danger of damage as the wheel is stationary.
Click to expand...