Spacing for a triple on any bike less than 9spd is an old and long-lived standard; it should shift properly if the cable is clamped properly. Different chainring spacing is only narrower.

The cable runs over the top of the clamp bolt... I suspect you're going under it.

For a tidier look, you can pull the cable all the way around the bolt so it points down behind the seat tube, but this is fiddly.