Okay, the answer seems to be as follows:
1. Verkhovna Rada adopted the Constitution of 2004, which lets it appoint the Cabinet of Ministers (over 2/3 of MPs)
2. Verkhovna Rada fired the Head of VR and appointed Turchynov as Speaker.
3. Verkhovna Rada ousted Yanukovich (political decision). Turchynov under the Constitution became temporary President.
4. Verkhovna Rada voted for Yatseniuk as the PM under the new Constitution. Yatseniuk presented to the VR the ministers he’d like to propose (that were to an extent confirmed with the people on Maidan), and VR voted for the ministers separately.