Does that mean that
- the wind will be coming from south-east (since wind direction is usually reported by the direction from which it originates)
- the wind will be blowing to south-east (which is how I'd intuitively interpret "auf")?
In German the wind direction ("Windrichtung") is described in the same way as in English. In both languages the direction given is the direction the wind comes from.
In your example however we see the verb "drehen" with the preposition "auf". This indicates there was a change of wind direction but still the direction is where the wind comes from:
Yes, it means that the wind comes from south-east. Here are some other alternatives to say from where the wind comes.