So Duettist allows your familiar to perform separately from the bard and to perform simultaneously, stating:
Performing Familiar (Su)
At 4th level, a duettist’s familiar learns how to create supernatural effects with its performances, just like its master. The familiar can use any of its master’s bardic performances, but only the familiar or the duettist can have a performance active at any given time, not both. If one is performing and the other starts a performance, the previous performance immediately ends. Each round that the familiar performs consumes 2 rounds of the duettist’s bardic performance.
Harmonizing Familiar (Su)
At 8th level, the duettist and his familiar have learned how to perform together in harmony. When a duettist and his familiar perform the same bardic performance simultaneously, its effects are enhanced. If the performance has a DC, the DC increases by 2. If the performance provides a competence bonus, the competence bonus increases by 1. Because both the duettist and the familiar are performing, each round performed consumes 3 rounds of bardic performance.
Now this makes it seem like its performance is separate from the bard's, and I am wondering if Saving Finale would end only your performance when its cast as it says:
You must have a bardic performance in effect to cast this spell. With a flourish, you can immediately end your bardic performance when a creature within range affected by your bardic performance fails a Saving Throw, allowing the subject to immediately reroll the failed Saving Throw.
So if me and my familiar perform simultaneously and I cast Saving Finale to let someone reroll, does my familiar continue performing or do we both cease performing?