I've done this both ways (on and off the hammock suspension). Done right both work. Most of the time I prefer off for two reasons

1) I tend to a bit larger tarp for coverage in really foul weather. it's harder to do the on the suspension thing with a big tarp.

2) I carry lines for my tarp anyway, as there's a good chance on any of my trips I end up above the treeline and tarping it.

but I suspect a lot of the preference is the environment you hike in - at least I think it is in my case.