The short of it is that later on and in team fights, Jinx just wants to stay in rocket form. There's no reason to go into minigun. There's no way to switch to minigun to show skill expression. Being in minigun form costs you waveclear and safety. Phreak is right, Jinx needs incentive to be in minigun form.
I have some options for riot to consider to allieviate things a little so she might want to be in minigun form. Note all of these ideas should be considered separately and not as a group.
1. Have minigun crits either trigger her passive or give her bonus MS as she stacks AS with it. Basically if she's giving up safety in terms of range, let's give her a chance to move about the battlefield and reposition better. Riot would have to be a little bit careful with the numbers though. If not by cirt then maybe every 4th attack in minigun form gives her bonus MS.
2. Let the minigun damage scale a little with AS. Basically as you stack it up you do more damage, enough to consider switching out of rocket form and into minigun form. This could be on hit damage that scales with AS, a little bit of armor pen, crit damage multiplier that scales with AS, the old MF W passive where she does more damage the more times she attacks the same target with her minigun, etc.
3. Maybe give her armor/mr in minigun form that scales with AS. Basically instead of being safer by range, she now has safety in terms of a little beef. Ideally the amount of armor shouldn't be much more than a lethality an assassin has. However I'd also reduce her mobility in this form a little.
4. Give her sustain in minigun form. This could either be a little bit of on hit healing (+2 life per rank) or on hit mana regain coupled with a slightly higher cost cost for her rockets.
5. Give rockets a limited supply of ammo instead of costing mana and have attacking in minigun form speed up their recharge. This idea would be pretty rough on its own and would do a lot to change her playstyle so it'd probably need other changes to go with it. But the rockets could be better.
6. Lower the base damage of her rockets, give them bonus damage against towers and epic monsters, and against other stuff let them put a stack of armor debuff on champions (max 3) that only her minigun can make use of. With this idea, her rockets are still good against big stuff and against champs, they are mainly a tool for softening things up. Doing this would kind of encourage Jinx to go into minigun range to make use of the debuff.
7. Move the AoE from the rocket to the minigun. Basically make make the minigun like grave's shotgun where it sprays bullets everywhere but she doesn't need to reload. I think that a bullets everywhere fantasy would work great on the weapon and with jinx in general.
8. Give rockets % armor pen and her minigun a little physical % max health damage. This idea means Jinx would want to use rockets only against opponents that have stacked armor primarily while switching to the minigun for squishies. This means jinx players would need to know who to use which weapon against for best DPS.
9. Get rid of the rockets mana cost but have 2 different optimal build paths for rockets and minigun. For example the rockets might have reduced AS but have bonus armor pen when you crit, or they are like Ashe and they always crit and the amount of bonus damage goes up based on how much crit% you build, while the minigun form applies on-hit damage twice every 4th attack. So this way you'd have minigun jinx players, rocket jinx players, and hybrid jinx players.