I can't speak to "touching a POI from search", but I do know that tapping on a point on the map screen - whether a track point, a waypoint or long pressing on a location - which ends up bringing up the popup, will leave auto-centering on while keeping the map screen focused on whatever you last looked at. I believe even if you drag the map to another location with a popup open, the screen stays at that location despite the fact that auto center is enabled. You have to tap the screen again to "close" the popup in order for auto centering to snap back to your location. I've had that happen numerous times on rides before. It's a minor annoyance, but it makes some logical sense. It's a bit of a grey area whether it makes more sense to snap to location while a popup is open, or leave the screen in the last location.