For that to work the value of s has to be saved to s for every loop

s += tmp is short for s = s + tmp. So, s + tmp is literally saved to s for every iteration of the loop. This expression is not "inside a function call". The result of the evaluated expression (s) is used as an argument to the function.

Any code of the form:

    someFunc( s += tmp );

can be rewritten as

    s += tmp;
    someFunc(s);