When I run my python script (content irrelevant for this question, just uses print a couple of times) interactively, it sends the output straight away.
When I use it in a pipe to tee or in an output redirection (./script.py > script.log) there is no output. What am I doing wrong?
I suspect you're encountering output buffering, where it's waiting to get a certain number of bytes before it flushes. You can look at the unbuffer command if that is undesirable for you.
As it turns out, Python detects whether or not you are using a tty, and increases its buffering when you are not. Several options on how to disable this can be viewed at this question.