Here's a simple idea that reflects what I do with my account, more or less:

Each time I get my salary paid, I want the full amount of the payment to go into one account (let's call it "main") and then the previous balance of this account to be transferred to another account (let's call it "savings").

That sounds a bit confusing, so here's an example:

My salary is 1000 EUR. It's the end of the month, but I've been good, and "main" still has 300 EUR in it. My salary arrives. This remaining 300 EUR now goes to "savings" and "main" gets topped up to have a balance of exactly 1000 EUR (ie: my salary). In this way, I have my monthly salary available for spending each month (in "main"), but at the end of the month, anything that I didn't spend gets moved over to "savings".

A very similar feature could be to specify that incoming salary payments will top up a given account to a particular amount and then the rest will go to another account. This is different than the current salary splitting feature because that feature isn't dependant on the current balance of the accounts in question.