"Creation" and "Modification" dates bear no relationship whatsoever to the image "Capture" date, aka "Date Time Original". The first two are dates (and times) created by the Operating System, and reflect the time that the actual file was written to disk, and was last modified. Initially these two dates will be identical. The "Capture" date is created in camera and stays in the Exif part of the file header on your original files, and is also included on a derivative file (e.g. a jpeg export) unless you specifically choose NOT to include metadata when you export.
Assuming you DO include the metadata when exporting, then the "Capture" date will still be available in the exported file header, and can be viewed with an appropriate viewer. Using WIndows Explorer it is possible to amend the 'standard' file details view to additionally include a lot of additional data from the file header, including the date the image was taken. See here:

I'm not sure if Finder has the same capability to show the "Capture" date, however....you may need a more specialised file browser for that. But first you need to ensure that you ARE including the file metadata on export....