There aren't any secret tags, but there isn't a standard either, so there are lots of different implementations. Looking at the two files, they are not identical, not even visually/textually.
What is noticeable in ORprecipnormals.csv is that every numeric is exactly 2 decimal places, even when the number ends in a zero, i.e., 18.40 instead of 18.4. In and of itself, that is not causing the issue you are seeing, but it does make me believe that the Excel table had number formatting turned on when the CSV was exported.
When number formatting is turned on, it has been my experience that Excel treats formatted "numbers" as text when exporting to certain formats, CSV included. In this case, Excel has added an extra line to the end of the file. If you open up and look at ORprecipnormals.csv in a text editor, you will notice the last line doesn't contain actual data, but a series of underscores separated by commas. It is this last row that is being used to convey formatting information back to Excel, and also Pro, when opening up CSV files.
If you open ORprecipnormals.csv in a text editor and remove the last line, it will load the "numbers" as numbers. But, and this is a big but, the overly aggressive caching mechanism of Pro will continue to see those numbers as text even if you remove and add the file back into the application. If you remove the last line of ORprecipnormals.csv and rename the file and then load it, you will see it load as numbers.
Personally, I consider the caching issue/behavior I described above as a bug, I just haven't gotten around to chasing it with Esri Support.