If you enable “Snap to Fine Grid” and set the fine grid divisions to 2, then your points will snap to both the centers and the corners (and the centers of the edges) of each tile. It’s not exactly what you want, but I think it will help you place those points in the center.
And indeed, like @Modanung suggested, shifting the object layer by half a tile using the Horizontal/Vertical Offset (in Layer Properties) would also let you snap them to the center. I guess the main downside is that you’ll probably have to change your game code to apply the offset there as well.
Of course, a “Snap to Center” could be implemented. Actually a much more powerful grid system could be implemented, since objects are not limited to the tile grid and even for tiles additional grids can be useful. So far I have not placed this on the roadmap, but it’s something I’d like to see eventually as well.