The issue is related to the 'CellSizeTollerance Factor'. The default is 0.8. It essentially means that if imagery has differing resolution and factor between the pixel sizes is > than this value, the system will pick one (the nearest to the current display). In this case you have pixel sizes that are a factor of 2x different. If you change this value to 2.5 and then re-run 'Calculate Visible Items' the issue should go away. The system will then assume that you want to see these differing resolution image as the same time.
Its not clear to me why you wish to use 'Minimum' as a mosaic method in this case. It is likly to cause strange artifacts in the image as for overlapping pixels the pixels with the lowest value will be selected. As the images have different resolutions you will get a mix of resolutions back, also darker objects (eg shadow) get a preference to lighter object.
You should be able to just define the mosaic method as first.
What you will want to do is still remove the white. There are various options
1) Just define white as NoData - Works but not optimum and if the original data is compressed then you may get compression artifacts at the edges
2) If there is overlap between the images (which I assume is the case) then even better is to 'Recompute the footprints' with a small 'Shrink Distance' and set 'Maintain sheet edges' on. What should happen is that the footprints will be redefined to exclude the white areas. You can then set in default properties: 'Always clip to footprint' to Yes, and 'Footprints may contain NoData' to No. The system will then clip the images based on the footprints.
3) You can use the 'Build Seamlines' tools. These will perform an analysis of the overlapping areas and generate seamlines along which the image can be clipped and also blended to hide the transition.
Once you have got this working at the larger scales you will probably want to regenerate the overviews.
