Which one is true about sunflowers, "follow the sun across the sky" or "always face east"?
Both are correct. 

The issue here is the developmental stage of the flower, that is, if it is a immature or a mature flower (actually, not a flower but an inflorescence instead).

Immature or young flowerheads do display heliotropism. However, as the flower matures, it stops showing heliotropism and becomes "fixed", always facing east.

This is a photo of the sunset. If the mature flowers (or inflorescences) still displayed heliotropism, they would be facing the sun (at the west). However, they face the opposite side (east):



Also, to be honest with the sources, the first link (Science ABC) you provided does make that clear. You can read next to the end:


  Mature sunflowers finally stop displaying heliotropism.


So, there is no contradictory information here.

A good source of information, with videos, can be found at this page of Berkeley University, which says:


  As the sunflower matures and the flower opens up, overall growth slows down and the plants stop moving during the day and settle down facing east. This seems to be because, as overall growth slows down, the circadian clock ensures that the plant reacts more strongly to light early in the morning that in the afternoon or evening, so it gradually stops moving westwards during the day. 




Source: https://nature.berkeley.edu/news/2016/08/sunflowers-move-clock