Difficult to answer which one is correct, both sources are prone to offsets.
But there’s an solution: Make sure there is a known point (or points) on the island (determined by GPS traces) and rectify the Tiger data based on these points using one of the offline editors (JOSM or Merkaator).
If the Tiger data is rectified then you can rectify the satellite imagery to the Tiger data (using shift-drag if I’m correct). If all this is done then you can start mapping using the satellite images.
Ok. I am now convinced that the Tiger data were wrong. I made quite a mess out of Samoa, but at least the Coast Line, The Runway an the one hand drawn high way are back were they belonged. Are the missplaced Tiger Data worth keeping (most street do not bear names or are plainly wrong) or would it make sense to delete the streets and try new?