I have seen this quite a few times in-game now. When I spy on someone or when my fleets reach another player the (*) appears next to his name. It should mean that he is active, yet actually he is ofline. And then after 10 minutes the (X m.) appears. Why is that. It shouldn't be counted as activity so why does it appear?

It means activity has occurred on that planet, not that it was that player who caused it. Anyone who probes or attacked a planet will cause activity.