This is not solved. This should be an option in the settings UI of Resylio Sync, not something that requires a change to global behavior in system settings or a registry hack. If google sync, dropbox, even my shareware audio manager can do it, so should this software. It has nothing to with the windows version: any of them has a way to start an app in the background on startup, i.e. as system tray icon. Whatever default behavior was introduced by a recent windows update, these apps found a way around it.
You might tell me it is hard to do with your current codebase, but it is certainly possible and expected from sync apps to start silently, without popping windows on startup.