WinSCP synchronization does not compare file contents. How could it do that? Most FTP/SFTP servers do not support calculating file checksums. Without that, comparing file contents could be done by downloading complete contents only. Then, the synchronization would have no advantage over mere complete directory download.

Having that said WinSCP is newly (since 6.0) able to make use of shell (if you have a shell access to the server) to calculate file checksums. Eventually, we plan to make use of that functionality for synchronization. You can vote for it here:
Issue 52 – Use file hash as criterion for synchronization

Also, I do not understand why you blame WinSCP for incorrect timezone of your server. Have the server fixed.

I'm attempting to synchronize files from a folder on Linux to a folder on Windows 10. While a manual inspection of any given file will show that they are indeed different, it always says "No differences found." I realize that the timezone of the Linux box is incorrect, putting it about 7 hours behind my Windows machine, that is pretty silly that WinSCP refuses to acknowledge the different binary data present between the two machines. There should be an option to do a more rigorous comparison, or ignore the timezone or something.
As it is now, I'm about to give up on this application and manually copy them all myself every time.