The Alexander family is very much part of the trial, legally and otherwise. In the eyes of the law, they are victims, and have certain rights under the Victim's Bill of Rights. This includes the right to be present at, and included in, all parts of the trial where Arias has a right to be present.
http://www.azleg.state.az.us/const/2/2_1.htm
Also, the jury is well aware of who they are, as Stephen and Tanisha have given Victim Impact Statements in this penalty phase retrial. They may have known who they were through media seen
before they became jurors - knowledge of the case was not a bar to jury service if they believed it would not affect their ability to judge the case on evidence presented at court.
ETA: Personally I read "favor the Alexander family" as meaning it was hoped that their decision would
happen to be a good one for the family, not that their decision would be unduly swayed by the family.