[Moved to Ask a Question - Android Apps is for app developers]
Smart Switch doesn't look for an SD card, it restores to internal storage. By restoring a file, the creation
and modified dates are the date Smart Switch created the file on the new phone. If you can find a Touch program (it would run in Linux, the kernel for Android - and the phone would most likely have to be rooted), you can touch all the files with the original dates. Or, you can try
Recover the date of medias after copy (it's free for 50 files at a time or, for "a small fee" [the developer doesn't say how much], for an unlimited number of files). (But try the free version first - it only modifies the MediaStore database, and I can't guarantee that doing that will make the files appear to picture apps [like Gallery, Google Photos] to have the correct date. If it works, you may want to pay for it.)
Copy them to the SD card first, though (don't use Move - if that blows up during an operation, the only copy of the picture could be in RAM, and you lose it), check if each one copied correctly, then delete the originals if they did. Then restart the phone (to rebuild the MediaStore database - copying files doesn't do that)
then run "Recover the date of medias after copy". If you correct the date, then copy them to the SD card (or even move them - which is just "read into RAM, delete the original, write the copy to the new location"), the files created will have the date you did the copy.