If the attached image is the one you exported, then it is 360 x 360 px. If you engrave it at 0.1 resolution it is 36 x 36 mm.
Images don't have physical dimensions, unless you know the resolution they are going to be displayed at (or printed, engraved).
So to make it 101.6 mm, and engraved at 0.1 resolution it needs 1016 pixels. If you change the resolution to 0.2 then it is going to be twice the size and engrave at 203.2 mm.
You should use black/white mode for a logo like that, not dithered.
How are you doing the trace, are you using Sketch Plus or doing it manually? If you have relocate origin enabled it will shift the trace to lower left and not align.
JPG, BMP and PNG are image formats.
DXF, PLT and GBR are vector formats.
PDF using Agastar's utility will extract vector information only.
Edit: Attached image with raster and vector (trace) combined, using SketchPlus and verified correct alignment.