It is possible to see the flush buffers dialogs from 4D Remote:

Here is why:

The structure file in 4D v11 SQL is also a "database". That is, 4D uses the database engine to manage parts of the structure file. This is also true for a client, because there is local copy of the structure file (in the user's profile folder).

The cache is an integral part of 4D's database engine; the point being not only is there a data file cache, there is also a structure file cache. So the reason you might see the flush buffers window on a client is because 4D Remote is flushing the structure cache.

Now, you shouldn't normally see it because the structure cache is quite small, so the flush should be fast. But in environments with a lot of users, or on slow hardware, it is possible the flush will take long enough for the dialog to appear. That is to say, the dialog only appears if the flush duration breaks a certain threshold (this is true on the server as well, and true of other 4D dialogs like query progress dialogs and such).

So it is definitely possible and definitely not abnormal to see the flush dialog on a client.