The assumption is that if you call out "on your left" the person actually hears that and not some garbled noise because of the wind. Any one looking back to the left will tend to move left slightly too so don't be surprised if they move to the left as they look back to see what that hell that noise they thought they heard was.
I treat it as I did when downhill skiing, the person in front has the right of way and you need to assume the responsibility not to run into them. Calling out "on your left (or right depending on the country") may not help much though if it is a long line of riders indicating that there is a group might be helpful if the first in the group as he/she is beside the overtaken rider tells them that