Nagi Makiko's Dragon Eye

It's an early trans but what she ment is that she's surprised that there is someone else than her that has the Dragon Eye(cuz Shin and his parents are dead).

http://www.mangafox.com/manga/tenjou_tenge/c024/

http://www.mangafox.com/manga/tenjou_tenge/c024/2.html

Here she used it again:

http://www.mangafox.com/manga/tenjou_tenge/c054/23.html

Here that dude realise that she has it, also due to rumors:

http://www.mangafox.com/manga/tenjou_tenge/c061/6.html

^She wasn't using it but she might have use it during their fight:

http://www.mangafox.com/manga/tenjou_tenge/c061/3.html

Here she noticed that Tsumuji snaped silently:

http://www.mangafox.com/manga/tenjou_tenge/c061/25.html

http://www.mangafox.com/manga/tenjou_tenge/c061/26.html

http://www.mangafox.com/manga/tenjou_tenge/c061/27.html

http://www.mangafox.com/manga/tenjou_tenge/c061/30.html

Here again:

http://www.mangafox.com/manga/tenjou_tenge/c081/12.html

And here:

http://www.mangafox.com/manga/tenjou_tenge/c121/2.html

There might be more but I don't have time anymore.

It's something else, much like Sohaku's "magical" abilities; it's not possible for her to have the Dragon's Eye since the only person that had it besides Aya was Shin, which he had until death. If she had the Dragon's Eye it would have come from Shin, meaning he would no longer posses it, which wasn't the case.

The only possibility would be if she had gotten it from one of Shin's parents, which also isn't the case since they were murdered by Shin before he was brought to her by Sohaku to "eat"... I'm referring to the time when Aya was watching the past and Dougen intervened.

She could've got it from one of the Natsume branch family.

the family branches don't possess the dragon's eye....

We don't know that for sure since we only saw one of the Natsume family branch.
What we do know is that they can have the powers of their main family(like with the insects).

http://www.mangafox.com/manga/tenjou_tenge/c083/23.html

It seems that she don't have it but how can she see the things I listed in the OP?

probably onmyodo? she's a magician, like souhaku, after all...

^^Exactly, the fact that she doesn't have the Dragon's Eye or a strong body and is so well versed and powerful makes her that much more awesome though, it just sucks she got used so hard and ended up dying in the end...