These are only there to help blind people cross the road. They have no influence at all on how fast the pedestrian light will turn green [1].
They also don't vibrate or give any auditory signal (except when the actual green walk signal comes)... I'm not sure how a blind person could use it because their sensitivity is so low that you have to keep touching, pressing, smacking the touch surface until it registers you and updates the (purely visual) signal on the other side. I ended up just crossing illegally at one crosswalk because the damn thing just wouldn't work.
If they don't have the three dots in the circle they usually do control the lights. Newer models also show a red light on the side of the button when pressed, similar to the UK lights just more subtle. But there are also plenty of old buttons around that don't.