Non-physicist here. If the modulation is annual, does that imply that the Dark Matter they're detecting is stationary, relative to the Sun (meaning it orbits the Milky Way on the same path as our Sun)?
If it helps, think of your car's tire as you drive down the road at speed v. The part of the tire that touches the road at any instant has no speed (relative to the road), and the opposite point on the tire is travelling at 2*v (still relative to the road).