It may be an issue similar that reported here: Lightroom CC: JPEG format tripping up other programs
Can you upload a sample TIFF that has this problem to Dropbox (or similar) and post the link here? I can then see if it has the same issue as described in the post above. (JPEG and TIFF metadata has a very similar encoding.)
Here are four files of the same image in different formats. In MediaBin, which is what our company uses as an digital asset management database, only the TIFF version does not display the caption metadata and copyright, which is critical for our archiving purposes.
It appears that this is caused by the same problem described here: Lightroom CC: JPEG format tripping up other programs. JPEGs and TIFFs use the same layout of metadata, and I confirmed that your TIFF has the same atypical layout as LR-produced JPEGs.
The issue is not that LR has a "bug" -- the TIFFs and JPEGs it produces strictly conform to industry standards. Rather, it's that there are many programs out there, evidently including HP MediaBin, that are buggy and don't conform to the standards and get tripped up by the atypical way that LR writes its metadata. Of course, Adobe can't change all such non-conforming programs, so LR users would very much prefer that LR go back to using a more typical layout of metadata.
Please add your vote and opinion (with details) to the bug report linked above. The more people complain, especially professional and commercial users, the more likely Adobe will prioritize a fix.