Screen sharing activates screensaver/stand by on client machine

I installed Capitan on 2 machines - one is part of my private network, the other one of the office network. Both machines act in a strange way that I can't remember from previous versions of OSX installed on these computers: Every time I connect to these "new" machines by screen sharing (from an Imac or Macbook) they automatically activate their screen saver (private machine, Mini Mac) or stand-by-mode (office machine, Mini Mac too) as soon as I close the sharing window and disconnect. This is pretty annoying!

Does anybody else have experienced the same issue, and/or have a solution for this problem?