This is a major problem that I have encountered as well, on all of my machines that have High Sierra installed. File sharing is either significantly different from what it was pre-High Sierra, broken since the introduction of High Sierra, or both.
It is absolutely absurd how badly damaged (or different) file sharing has become since this update. I use one of my computers (a MacBook Pro) as a glorified hard drive, and I require it to be a reliable share for access to my collection of projects for my clients, as I do a large portion of my designing from other computers — computers that connect to its hard drive. The only way to connect now is to go through an IP address, as clicking on the icon of the device in the lefthand side of a Finder window no longer works as far as establishing a connection.
This newly-forced type of connection is wonky as heck, and of course when connecting this way, we get all kinds of anomalous file-writes, such as this thing we're discussing here with the temporary files being created and then not disappearing once the save has completed — and then also not being able to delete them unless you're on the local machine where those temporary files are located. It's a mess, to say the least.
I created a help ticket in late-October/early-November, and have literally zero ambition by Apple support to rectify the issue. As a multimedia designer who relies heavily on file sharing, my workflow is severely hampered.
What the heck is going on here, Apple‽