I guess this is also what @YuuichiTam wanted to say, that ～時 only means literally "the very moment" the verb takes place. When you do something a breath after the action, it is no longer in the expression's scope. For example, you could say:
When I ate the apple, I immediately noticed it's rotten.
A bite of it immediately brought me back memories of good old days.
would perhaps mean that when you put the last piece of meal into your mouth, you suddenly find yourself outside the door. That's pretty futuristic. But if you want to follow the traditional method of putting the fork down and walking from dining table to entrance on your feet, you must say: