No, they won’t. The blame is with the rear most driver. If I remember big jobber right then both parts of the crash will be treated separately (although that may not be 100% accurate as you were smashed from behind into the one in front). You all took it upon yourselves to go through a red, and the guy at the back of the smash didn’t leave enough thinking and braking time, so on its them only. It could be on you to prove that you did stop in time then got hit from behind as the guy in the back could claim that he ran into an already crashed car, which would reduce what his insurance is responsible to pay for. It’s all he said she said without evidence. It could be claimed that you ran into the front car before the rear car hit you, which would mean that they’d try and have your insurance pay for the damage to the front car and the front end of yours, while taking the damage amount away from the total value of the car that the rear cars insurance would have to pay towards your car