Normally, you can summon entities and give them custom nbt with /summon. However, when you try to put in a custom value for FireworksItem, which determines things like explosions, it gets deleted when the firework is summoned, and so the rocket doesn't explode.
I am testing this with the command
/summon minecraft:fireworks_rocket ~ ~ ~ {Life:1,LifeTime:50,FireworksItem:{id:"minecraft:fireworks_rocket",Count:1b,tag:{Fireworks:{Flight:1b,Explosions:[{Type:1b,Colors:[I;3887386,11743532],FadeColors:[I;3887386,5320730,2651799]}]}}}}
which makes a rocket with the entity data at the bottom
the item id is firework_rocket, not fireworks_rocket; if the id is invalid, the item is invalid, and as such the FireworksItem tag is removed.