Hi Matthias,
Sometimes values do not re-calculate itself and would need to add more logic and use a hidden field. Could you try adding a hidden field, with an action that sets another field's value (to any value you desire). Set this hidden field to the value of the people picker's account ID (assuming that the user can only select 1 person), and add the condition to the rule that the action should only run if the hidden field is not blank and the hidden field is equal to the current user. If this doesn't work, please attach a sample of your form so I could run some quick tests on what isn't working for you.
Regards,