Jinx, when to use rocket or minigun

Well there is no specific time to use one over the other in terms of early/late game, it depends on the situation during the moment. Rockets are better for teamfighting, as long as you can stay far enough away to stay safe. If someone gets up close to you, switch to minigun, as you have higher DPS

Well it depends on her positioning and the job she tries to do.

While Rockets are better for poke, long range AA snipes and teamfighting in close enviroment, using the minigun is more profound for kyting, waveclearing and all-Outing someone.

Jinx is a very adaptive carry, and honestly im a low elo scrub so my word won't mean much but with jinx i would save the rockets for pokes vs someone who tries hard to push you out, trading inlane earlygame and farming backlines.

Fight teamfights in closed enviroments like the Jungle. Your rockets will shine bright in that scenario, but be careful to get your passive off first. Your rockets are good for AoE dps and Extended burst but you still attack slow as fuck.

honestly their use varies very strongly, too much to give you set patterns. but what i can do is suggest you some best and worst scenarios

Mini gun for DPS, Rockets for Wave clear, AoE damage, and Range.

From close range to long range you have: Mini Gun, Rockets, Zap, Ult. My advice in a teamfight is to attack the closest target you can reach safely, using the closes range weapon that can reach him.

Rockets when your trying to hit a bunch of clumped up people in a 5v5, mini gun when you have an immediate threat (tank, vi) that you have to deal with

Also mini gun on baron/dragon/objectives always

Also, once you have stacks of get excited it usually means the enemy team lost the fight and is trying to run away, switch to rockets so you can Chase them down