Why did Historia see her father's memories? In Season 3 Episode 9 we see that 


   after slaying her own father, Historia gains access to his memories.

 


According to Season 3 Episode 6 and Chapter 89, 


   titan shifters are able to see the memories of their past and future holders. (read here for explanation)


Historia, however,


   has, up to this point, never possessed the power of the titans.


But we do know from Season 2 Episode 5 and Season 3 Episode 2 that


   she has blue blood which means she can use the Founding Titan's abilities to its full potential. (not exactly full, but at least more than Eren)




Is there an explanation for this?
As far as I know, it was never discussed as of the release of the most recent chapter. That specific scene in Chapter 68 was mostly what happened in the anime. It could be explained in a future chapter. 
Looking closely at Episode 9, 


   it can be seen that after the flashbacks of her father's memories, Historia opens her eyes as if surprised at what she saw. This might mean that her eyes were closed during the flashback scenes, implying that she saw her father's memories.


In the manga, this was not exactly what happened. 


  She just widens her eyes and opens her mouth slightly as he killed him and as her father's memories were shown. From my interpretation, it could be that she was just surprised at what she had done.