Altium: Routing in different layers brings me back to top layer
To enable snap to any feature on any layer, especially during interactive routing:

Press D then O (Design, Board Options), then click box next to "Snap On All Layers".  This will allow snapping to anything, any layer.  Make sure snap Range is not set too large, else routing becomes a nightmare.

Another shortcut is press "Snap" button lower right corner of active pcb layout window (".pcbdoc").

Be careful of what you wish for...