First, just checking that you realise: the "blue" is just shadow warning indicators, and these would never be expected to appear in the exported image.
If you want to illustrate these shadow / highlight warnings e.g. for posting on the web in some kind of technical discussion, you could maybe do a screen-grab of the image - just as it is displayed within the Lightroom Develop module.
That aside, one reason why exported images sometimes seem not to show adjustments made in Lightroom, is when "original" has been selected for the file type. In this case, for e.g. a Raw file, the exported file will be a Raw file too, with LR edits appended in metadata. If the method being used to view this exported file is not able to take account of the appended LR edits (does not "understand" them), then they will duly not be evident on screen.