Temporally entangled particles seem to show purpose, but consciousness is required.

When you put on your shoes before you go for a walk, the cause of putting on your shoes is going for a walk. The cause comes after the effect. This is called final causality. Final causality indicates purpose.

In nature there is mostly efficient causality: the cause comes before the effect.

But with temporally entangled particles the cause can come after the effect.

Does this mean purpose and consciousness can be explained by naturalism?

No because ...

There must be an observer in order for the entangled causality to occur and physical processes cannot observe anything. So the very occurrence of reverse causality at the physical level means there is top down influence from the human level to the physical level. Not only is quantum physics unable to explain human final causality, it cannot explain its own final causality by itself. Its final causality is a trickle down effect from the human level.
What's true it seems is that only life has intention, so only life can be conscious and this consciousness separates us from the scenery, that is to say it's a distinction that matters.
At a level of my being, I get "only life has intention" but I add one more force. I always viewed everything boiling down to these two forces. A life force and an anti-life force. And the delicate balance that gives life one tiny advantage over the other (that life was first) is what keeps the game going... and that the anti-life force (the "counter intention") is what keeps it interesting.