Auto snap to the selected component when press "M,S" in Altium
Sounds like your grid size is too small on the PCB. If you change your grid size on your PCB to something higher, you should be able to snap to whatever the grid size is. 

If you press G when in the PCB editor, and you change your grid to something large, like 100 mil, and zoom in so you can see the grid, you'll see that your components snap to the grid in 100 mil intervals.

If you change your grid smaller, like 10 mil, then the snapping will happen for every 10 mil grids.

Edit

So after the comments explained more, I have a similar setup, where I either split screen between Schematic/PCB or have each on its own monitor.

This is the way that I do it. 

Select component in Schematic (this highlights the component in PCB editor).
Move cursor to PCB editor windows, and drag the window. This is to switch the context menu from Schematic editor to PCB while keeping the component selected. If you left click, you may lose the selection.

Go to tools->component placement->reposition selected components (I have a keyboard macro that does this automatically, so its faster).

This will now move the selected component no matter where it is.

Additional, you can select multiple components in the schematic editor, and use the same method, and it will automatically switch to the next component after you have placed it. So if you are placing a micro + decoupling caps, you can do it all in more or less one go. It will also remember the selection order as well.