It's what I was taught: you switch on your indicators when you have checked that you are clear to merge and you have effectively committed. I always assume that someone who has put their indicators in is going to move according to them, whether it's clear or not.
I don't doubt that it's the way you have been taught, but it doesn't make any sense. The whole point of blinkers/indicator lights in cars are to signal your intentions before you do them: if you're going to signal at the same time that you do the action you're signalling, you might as well not bother.
It is what I see in practice in Eastern Europe. They signal as they are shifting lanes. Even if they turn the blinker on and then start moving 1 second later, it could be considered the same thing as 1 second is negligible.
Thus "the indicator shows that you ARE moving." is correct, at least in practice.
It's the difference between actually purposefully blinking and blinking to avoid a fine. In the latter you just tap the blinker stalk as you're turning the wheel. If someone's trying to do a dangerousish turn (waiting for a line of cars to do an illegal U turn for example) they'll be blinking to signal intention most of the time.
I got my license in 2014, in Germany, and was taught to turn on the turn signal > check mirrors > turn your head to look over your shoulder and only then, when you're clear, do you merge.