Yes and no; young sunflowers exhibit heliotropism. But mature sunflowers, those which have bloomed, will instead always face east. Thus the in game description is accurate, when folks think of the Flower turning to face the sun, they're thinking of a fully bloomed, mature sunflower with a giant open seed head. And indeed that will not turn to face the sun, it'll always face east. While young and growing and before it blooms you're correct, it'll turn to face the sun, starting out facing east and turning throughout the day before turning back east during the night to get ready for the next sunrise. Cool stuff, but the tl;dr is you're both right.