I've seen some post on this so this will be discussing why they acted or didn't act in Volume 4 episode 7 Punished. Story wise both reactions make sense to me.
Against Qrow's orders she joined his fight against Tyrian. This is the most reckless thing I recall her doing on the show. I've seen a couple of people praising it, I've seen many condemn it (although I'm pretty sure reactions would have been worse if it was another character.)
She points out it's her fight too and that she doesn't want anyone else to get hurt. While the first part is technically true (since Tyrian is trying to capture her) Ruby doesn't have an Aura to protect her. Which is very risky, so much so even Tyrian finds odd enough to comment on. The reason for her recklessness makes sense as we've seen her struggle with guilt over Pyrrha's death. Ruby wasn't there to save Penny and all she could do was watch as Pyrrha died. A big part of her character is her desire to help others and she feels like she's failing. She already lost two close friends, Ruby probably feels like she failed Jaune, her sister lost her arm and her team fell apart. Ruby doesn't want to sit by while someone else gets hurt or worse.
Sure JNR and her have been helping towns but otherwise it has to be frustrating. So much time has passed and their still not close to achieving their mission. The problem is that by joining in Ruby distracts Qrow because he has to save her from a trap he set up which gets him hurt. Possibly stung by Tyrian's venom.
Even so her actions make sense due to the plot. Ruby acts on emotion since someone she loves dearly is fighting for his life. I'm not saying it wasn't foolish but it's understandable.
On the flip side Jaune was the only one who didn't jump in the battle which actually made him the most sensible one. Jaune has previously rushed into danger before this volume something seemed to shift between 3 and 4. While I think part of his reaction has to do with fear of losing Ruby like Pyrrha I don't think that's the reason for him not joining in. I believe he shut his eyes in episode 6 since he suddenly felt that same helplessness again and felt that fear of loss when he yelled out to Ruby. His concerned is underlined when he asks why Tyrian was after Ruby.
I'm not sure if Jaune was going to rush in before Ren pushed him back but I think he clearly saw that Ruby was putting herself and Qrow in danger. Their building Jaune up as the strategy guy so yeah, I think he knew it'd be counterproductive to try until the moment Qrow saved Ruby/got stung. Also remember Jaune doesn't have a long range weapon and isn't as skilled as the others. He knows this all too well.
Jaune may not have all the details at the moment but when was in the vault he knew what being in over your head was like. He tried to attack Cinder which didn't work. Ozpin told Pyrrha (the best student fighter) that if she helped she'd get in the way then listed people that could help him, I believe Qrow was on that list which means he would have some idea of Ruby's uncle's skill level. Jaune KNEW Pyrrha wouldn't win against Cinder. So getting in the way of a professional would make no sense.