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Usually I get my DEMs and rastermaps from USGS The National Map client here in the USA.
So, DEMs in this case will be correctly aligned. With GeoPDF we have to be a bit more careful. I have encountered a few where georeferencing was wrong, for various reasons. Georeferencing parameters are part of the GeoPDF meta data. One possible mistake is the geodetic datum. While it should be NAD27 I found NAD83.
As you work with USGS 1/3 arc sec DEMs, you can usually verify your raster map, at least in hilly terrain, with the contour lines, or by turning on DEM shading. Map and DEM must match. Or create an overlay with the map tile client, and use OSM as the tile server.
Then, if DEM and raster map are in sync, and the vector input from JOSM is not, it's quite clear that something went wrong with the JOSM data. And that must have happened in one of the stages of the transfer workflow, because the OSM base data will be correct.