"In general, what happens to the DNA samples from the 159 innocent people? It seems like a violation of their privacy to keep those samples on file."
In cases like these, the samples of the innocent people are ordinarily gathered from information in which the innocent people do not have a reasonable expectation of privacy because the information has been shared with the public, or with people who have given law enforcement permission to use the information.
The investigators never get the actual physical samples, which are disposed of after they are analyzed by a lab. Instead, the investigators get a data file (really nothing more sophisticated than several pages of a plain text document) recording the alleles that a lab test of the sample voluntarily submitted for genealogy, entertainment, and self-understanding purposes to a commercial consumer genetics firm such as 23andMe (there are maybe half a dozen such firms).
Typically, the firms that offer these services allow for a variety of privacy settings, some of which would either make the data available to the public, or allow the data to be shared by people who are related to the person providing the sample or their relatives.
Also, while in the example you provided, one of the samples belonged to the guilty party, that wouldn't be necessary for this technique to work. A publicly available sample, for example, might show a second cousin relationship with the forensic sample. Then, the investigators could determine who the second cousins of the publicly available sample provider were and use that lists to narrow down suspects using other kinds of evidence (especially alibi evidence, i.e. determining which second cousins were alive, of the right gender for the sample taken, and could have been alive at the scene of the crime when it was committed while not too young or too old to have committed the crime).
The data could be disposed of in routine file destruction, but often wouldn't be as it would take up almost no space in electronic form.