Changing EXIF data when adjusting capture times

there are many different date and time fields within EXIF data so it depends which one you are talking about. For example, if you use the Edit Capture Time that will change some but others may still (deliberately) preserve the original date/time which the camera had recorded. Also there will be some manufacturer proprietary info fields which will not have been updated. Provided the right result then happens, e.g. so far as the "Date Taken" info reported within JPGs that you export, these other unmodified date fields simply do not matter.

Separate issue: for example the Edit Capture Time dialog updates the info in the Catalog DATABASE. This action is not the same thing as updating the EXIF data that is held by the imported image FILE. So if you inspect that, it may not have changed (and to repeat, if does matter which particular metadata field you are looking at). However, you can manually tell the Catalog to update (write out) its metadata to the external file. Also you can turn on an "automatically write XMP" option which makes this happen for each new change made (after turning the option on). 

Finally: neither the file creation date nor the file modification date has any necessary relation to the "date taken" - as originally, or as corrected - nor to the date imported, nor to the date edited.