I think on my new Mac, Stuffit leaves the downloads alone, on this Mac, they start to open right away.
You can change that if you want. Depending on the browser you are using, go into their prefs and find the download section where you can tell the browser whether to open or save the type of files you download. Each kind of file (jpg, sit, etc.) can have differing instructions.
It's actually safer to do the opening of files yourself later as it prevents anything from possibly opening and depositing a virus in the future. Granted there is little worry of that now but it's an extra security step to consider.