Hi kajak,
Here is my workflow which should solve your problem (start with an empty project):
1. Import images with GPS tags (WGS84)... I assume they are from a drone/UAV

2. In the reference pane, click the 4. icon from left (CONVERT)
3. Choose your (national) coordinate system to match the coordinate system of your markers/ground control points. The X/Y/Z coordinates of your images will be converted from WGS84 to your chosen coordinate system.
4. Import your markers. Both your images and markers should now have the same coordinate system.
Then process as usual. Don't forget to place the markers in your pictures. For photo alignment choose Reference. Remember to run 'optimize cameras' after alignment (magic wand icon in reference pane). You might also want to uncheck a few markers so they can be used as check points.
Let me know if that worked for you.
Regards
SAV