Why the server copy looks newer in FTP by Zaweba
FTP by Zaweba explains why server files look newer than yours: clock or time-zone gaps, servers that stamp upload time, or a real later edit.

Nothing is more puzzling than a warning that the server has newer files when you are certain nobody has touched them. You uploaded them yourself an hour ago. Yet the comparison says the server copies are newer, and it wants to download them over your work. FTP by Zaweba takes that puzzle seriously and explains each file, so you can tell a real change from a clock problem.
What the warning shows
For each file, the warning lines up both times, the difference between them, and whether the sizes match. Then it gives the likely reason. A summary at the top leads with the most common offset across the files, and the full table goes into the activity log so you can read it at your own pace or copy it out.
Seeing the sizes beside the times is often the quickest clue. If every file differs by the same amount of time and every size matches, the content is almost certainly the same and the clocks are the problem.
The reasons it gives
The first is a clock or time-zone difference. When two times are a whole number of quarter hours apart, anywhere from 30 minutes to 14 hours, the gap looks like a time zone or a clock setting rather than an edit. Servers are often set to a different zone from your PC, and summer time can add an hour on one side but not the other.
The second is a server that cannot keep file times. Some servers do not keep the time you send with a file and stamp the upload time instead. Every file you upload then looks as if it changed at the moment it arrived, which is later than the time on your PC.
The third is a server clock running ahead. A time in the future means the server clock is ahead of real time, and every file it writes looks newer than it should.
If none of those fit, the explanation is the plain one: the file was written later on the server. That is the case to take seriously, because it may mean someone else edited it.
Deciding what to do
If the summary points to a steady offset with matching sizes, the files are very likely the same, and you can untick them rather than downloading copies of your own work. If you want to be sure, right-click one and use Compare with Server Copy. The diff window shows changed lines, or none at all, and it settles the question in seconds.
If the reason given is that the file was written later, look before you leap. Compare it with your local copy to see what changed. If the site has the activity log turned on, Site Activity may show who uploaded it and when.
Whatever you decide, the tools that download are built to keep you safe. Get Newer, Sync and Get Recent all show a list before anything moves, and replaced local files go into the local history first.
Mistakes to avoid
Do not fight a time-zone gap by uploading everything again. On a server that stamps the upload time, every new upload makes the server copy look newer still, and the warning will come straight back. Understand the cause first.
Do not ignore a lone file in a long list. If thirty files share a two-hour offset and one does not, that one may be a real edit hidden among clock noise. The full table in the activity log makes it easier to spot.
And do not assume the warning is always wrong. Most of the time it is a clock problem, but the whole reason FTP by Zaweba warns at all is the occasional time it is not.