  When it then goes on to show Avi's future, I think that Avi is correct that she has accidentally broken the ter'angreal somehow. I think her talent is the likeliest cause, but it might also be related to her already having some knowledge of her ancestors' history.  This is where I get a bit more speculative: I propose that in extracting that data from the genetic memory of the previous users, it has had to store that information somehow. Then, when Avi breaks the ter'angreal, it malfunctions, and extrapolates a likely future based upon the information it presently has, plus the data Aviendha contributes, and shows her the future by showing her the lives of likely descendants. Because it's not designed for this, it then breaks.  Along this route of thinking, I doubt she broke it. I think she unconsciously reprogrammed it, something it was built to be able to do. Why would they build a tool that was simply a backward looking machine? 