My problem now is that I get error-messages if I want to compile the sketch for the ATTiny. As far as I understood, the library isn't compatible with the chip or am i wrong?
Well, I don't know. I think that you are wrong. But, I don't see that you posted the error message in your post. Or am I wrong? 
Where is the error message which we are supposed to be judging in relation to or commenting on?