It doesn't matter if the ball is travelling backwards, if you are ahead of the ball and there is only one opposition player between you and the goal line then you are in an offside position. I think the problem was that when the ball was passed across from the right, Coutinho was onside. As the ball travelled across, the defender moved forward putting Coutinho in an offside position however, I think the Lino thought there was another touch of the ball at that point, which there wasn't. Coutinho rang round to pick up the ball and that's when the Lino signalled and the ref stupidly blew the whistle. Had there been a second touch of the ball in the middle by a Villa player then it would have been offside. Unfortunately, once the ref blew the whistle, Man City players stopped and VAR could not get involved.
It is bizarre how in some case they allow play to continue when it is blatantly offside, eg Undav, and on others they flag straight away. Against Utd, we had a case where there was a close call for Welbeck and the flag went up immediately yet a similar instance involving a Utd player was allowed to carry on.
Bizarre yes but also kind of goes well along with the schizo fan/pundit take... when they wait with the flag, people are moaning about it, when they don't, people are also moaning about.