How to fix timezone of images using exiftool

This is a combination of exiftool FAQs #2 & #3. You are trying to write "Date" but that isn't the actual name of the tag that Windows reads. Additionally, Photoshop Elements may be reading yet a different tag. And to add on to all that, I believe that Windows and Photoshop Elements will read the time stamps differently.

To look at all the timestamps for the file, run this command:
exiftool -time:all -G1 -a -s File.mp4
That will give you the actual tag names instead of tag descriptions. It will also show duplicate tags and what groups they belong to.

I believe the three tags you mostly likely want to try to alter are the FileModifyDate, FileCreateDate (both System tags, meaning they're a part of the underlying file system) and the Quicktime:CreateDate tags. To change these you would use this command:
exiftool -FileCreateDate="2019:07:22 12:00:00" -FileModifyDate="2019:07:22 12:00:00" -Quicktime:CreateDate="2019:07:22 12:00:00" FILE.mp4

Here's is where you run in to the second problem. According to the spec, the Quicktime:CreateDate tag is supposed to be in UTC. Windows understands this and displays the time correctly adjusted to the local time zone. From what I understand, Adobe programs do not read it properly and assume that the time is local time, not UTC. So if the timestamp is written according to the spec, Photoshop Elements will probably not show the proper time.

The above command will write the Quicktime:CreateDate value exactly as written. If you want to write the value according to the spec (adjusted to UTC), you can add -api QuickTimeUTC to the command and exiftool will adjust the time to UTC based upon the local computer's time setting, or if you include the time zone in the value written, e.g. -Quicktime:CreateDate="2019:07:22 12:00:00-05:00", then exiftool will use that to adjust to UTC. In that example, exiftool will end up setting the time to 2019:07:22 17:00:00. Windows will then read it as 2019:07:22 12:00:00 (assuming your time zone is EDT, -05:00) and Photoshop Elements will read it as 2019:07:22 17:00:00.

One problem is the fact that the EXIF standard separates the date/time (EXIF:DateTimeOriginal) and the time zone (EXIF:OffsetTimeOriginal) into different tags. The subseconds (EXIF:SubSecTimeOriginal) are also located in a different tag.

Luckily, exiftool gives you a shortcut to write all three locations in a single command. You would use

exiftool -SubSecDateTimeOriginal="2022:12:12 12:00:00.24-08:00" /path/to/files/

This will write 2022:12:12 12:00:00 to the EXIF:DateTimeOriginal, 24 to the EXIF:SubSecTimeOriginal, and -08:00 EXIF:OffsetTimeOriginal at the same time.

Also of note are the SubSecCreateDate and SubSecModifyDate tags.

SubSecCreateDate writes to the EXIF:CreateDate (called DateTimeDigitized by the EXIF spec), EXIF:SubSecTimeDigitized, and the EXIF:OffsetTimeDigitized tags. SubSecModifyDate writes to the EXIF:ModifyDate (called DateTime by the EXIF spec), EXIF:SubSecTime, and the EXIF:OffsetTime tags.

There is also the XMP standard, which is much more flexible. It can either be embedded in the file or as an XMP sidecar. The XMP standard allows for all the data in a single tag. The command for writing to an XMP tag would be similar

exiftool -XMP:DateTimeOriginal="2022:12:12 12:00:00.24-08:00" /path/to/files/

Additional tags for XMP would be XMP:CreateDate and XMP:ModifyDate

One final thing to take note of for the XMP time stamps is that the Exif 2.32 metadata for XMP standard uses XMP:DateTimeOriginal as the corresponding tag for EXIF:DateTimeOriginal, while the IPTC Photo Metadata Standard 2022.1 uses the XMP:DateCreated as the corresponding tag.