First thing to know is that rules for processes with owner "System" or "Anyone" show up in everyone's Little Snitch configuration, and if they're changed in one configuration, they're changed in all. On the other hand, rules for processes with owner "Me" are specific to each configuration, and only show up there.
That means you could put "allow any incoming connection" and "allow any outgoing connection" rules for process owner "Me" in each of the other users' configurations, but not in yours. That way they won't get notifications about apps or processes they run, but you will.
You'd also have to put "allow any" rules for processes with owner "System" so that others won't get notifications about them. But that will affect you too. You won't be able to get notification of System-owned processes trying to connect somewhere. You could put in some "deny" rules if there are particular sites you never want the System to connect to, that nobody else needs to connect to either. But you'll have to know in advance what those are.
You could also disable the "allow any" rules for System every time you log in, and enable them again when you log out, as long as you remember to. That way you can get notifications about System-owned processes too, if you need it. Using a Profile could simplify changing the set of rules. There will be a short time between when you log in/out, and when you change the "allow any" System rules, that System-owned processes could connect without giving you a notification. It will depend on your situation whether that's a problem for you. Unfortunately there doesn't seem to be a way to change System rule sets or Profiles automatically at login, that I know of.