I always leave the lights on : it is my normal practice to leave the lights on. I do this every time.
I am always leaving the lights on: it is not my intention, but too often, I leave the lights on by mistake
In your example, 'Jim is always leaving things on his for' is correct
Sorry I can't really tell you why it means this! The inclusion of always is not just to add emphasis. It somehow becomes the focus. Because the statement implies something that is unwanted, it now means to me that you are frustrated with yourself that this occurs so frequently.
Hth