Dropbox keeps trying to download and sync files set to online only

Hi valtham and Rachel L. 
I too have experienced the same frustrating autodownloading of online only smartsynced files to my local hard drive. 
I also discovered that the autodownloading was occurring at a regular day and time of the week, althought the time seemed to shift by about half an hour each week. I run a desktop PC and a laptop on Windows 10 and both were experiencing the same autodownload but at different days and times of the week. 
After I noticed the pattern of the day/time that the autodownloading was being triggered I started setting calendar reminders to confirm the occurrence. Knowing approximately when it was going to occur allowed me to start and run Process Monitor and collect a log of what was happening on my systems at that time. The logs from Process Monitor (ProcMon) are extensive and build to a large (gigabyte) filesize quite quickly so its not really practical to have it running in continuously in the background, but it is possible. 
Another observation I had made with regards to the DropBox autodownload from smartsync was that the download appeared to always start with the top file in my folder structure.  My DropBox folder naming conventions all start with a 3 digit numeric followed by a folder name in characters. For example: 000_Images

So, once I had the ProcMon logs, that covered the period of time when the autodownload was triggered, i was able to filter the log for which processes were accessing the filepath for the top file in my folder heirachy. 
Following this approach on both my PC and laptop I was able to identify a process file called Inspect.exe was the being activated immediately before the Dropbox.exe  was actiated  to download the file. Inspect.exe is a Trend Micro (antivirus) process. 

Uninstalling Trend Micro does appear to stop the autodownloading of smartsync. 

I contacted Trend Micro about this issue over a period of a couple of months. At first they denied that inspect.exe was their process and then they didn't undertand how the online only function of DropBoc SmartSync worked with an 'image' of the local file. However, after many emails and sharing logs they acknowledged the problem and offered to make some file registry changes to see if that stopped it from happening. I wasn't too keen on someone poking around in my file registry and didn't want to rely on this in the future if I was to change devices so I didn't proceed with it. 

You might be surpirsed to hear that I actually 'learned' to live with the problem for the past year or more. I got into the habit of always loggng out of DropBox when I left my PC or laptop on and unattended for any extended period of time and on the occassions when the autodownload was triggered  again I usually lucky enough to see it happening and reset all the folders to online only and restart DropBox. This was still annoying and I never intended to persist with tolerating the problem. I had always intended on changing to another Anti-Virus software but never got around to it. 
However, last weekend I forgotto log out of DropBox and sure enough when I returned to my PC on Monday monring the harddrive was full and all my DropBox folders set to local. 
Hence, my motivation to check some blogs to see if anyone alse had experienced anything similar, which brings me here. 

Even though I have been a long term user of DropBox I was frustrated by the lack of proactive advice from the techs. Yes, they said it could be my Antivirus but without any further guidance I didn't know and still don't if changing to another Anti Virus software will not incur the same triggering of the DropBox SmartSync function. I would have preferred the DropBox techs to say "Trend Micro will trigger files to be synced to your local drive if you are using the online only SmartSync setting. I was actually more inclined to change my cloud storage from DropBox to say OneDrive or GoogleDrive than I was my Anti Virus because I did not feel genuinely supported by DropBox when trying to resolve this issue. 

I hope my response is of some help/comfort to you.