I think on mobile it’s natural to walk to the guy and tap on him. Not helped by the fact that the screen shows ‘tap’ over the highlighted tile, which does nothing. You need to walk and position the guy under your cursor, then press ‘act’.

The position yourself, then long press on ‘act’ to build when you can’t see where to put the building anymore is pretty awkward too. I’d expect to click to build, position it, then press confirm or reject or something.