(Edited per amended question. TL;DR: the setter made a fault of “reaching beyond the net”, signalled by the referee by a hand placed above the net, palm facing downwards.)
There are two issues when a back-row player sets near/above the net:
Whether the hit itself was legal: Did the setter touch the ball within his own playing space? Was it a proper hit? (Was the ball not held/caught/thrown)? According to your image, the setter touched the ball beyond the net, above the opponent’s court. In that case, the setter made a fault of “reaching beyond the net”, signalled by the referee by a hand placed above the net, palm facing downwards.
When the set is imperfect and the setter actually plays the ball towards the opponent’s court, it counts as an attack hit. And back-row players cannot complete an attack hit from the front zone when the ball is completely above the top of the net. This means that if the setter hits the ball completely above the top of the net towards the opponent’s court, it is an “attack hit fault” if the attack hit is completed, which means either the ball crosses the vertical plane of the net completely, or the opponent touches the ball.
But if the back-row setter touches the ball within his own playing area (or, theoretically, above the free zone, if the ball is overflying the net partially or completely outside the antennae), and plays it “backwards” into his own half of the court or parallel to the net or his teammate touches the ball prior to the ball crossing the net completely and prior to any blocking opponent touching the ball, it is valid play.
Relevant rules (see FIVB Official Volleyball Rules 2015-2016):
9: Each team must play within its own playing area and space
11.4.1 [Player’s faults at the net] A player touches the ball or an opponent in the opponent's space before or during the opponent’s attack hit.
13.1.3: An attack hit is completed at the moment the ball completely crosses the vertical plane of the net or is touched by an opponent.
13.2.3: A back-row player may also complete an attack hit from the front zone, if at the moment of the contact a part of the ball is lower than the top of the net.
13.3.3: [Faults of the attack hit] A back-row player completes an attack hit from the front zone, if at the moment of the hit the ball is entirely higher than the top of the net.
Cf. also cases 3.10.2 and 3.30 in the Volleyball Casebook:
Team A’s setter hit the ball above the net so that at the moment of the hit his/her fingers were in the opponent’s space. After the set the ball flew parallel to the net toward an attacker. The blocker of team B touched the ball in team’s A space, so that the team A player could not execute the attack hit. How should the 1st referee decide?
According to Rule 9, each team must play the ball within its own playing area and space (except in the case of Rule 10.1.2). Therefore, since the setter has hit the ball in the opponent’s space, the setter committed a fault. The blocker also committed a fault by touching the ball in the opponent’s space before the attack hit. However, only the first fault is penalized.
A back row setter jumped from within the attack zone and set the ball while it was completely above the height of the net, directing it towards an attacker. Before the attacker could contact the ball, it penetrated the vertical plane of the net where it was blocked by the opponent’s setter. Was there a fault?
Yes. The set became an illegal attack hit by a back row player when the attack hit was completed (in this case by contacting the opponent’s block). The rally should have been won by the opponents.