Nah, no need for extra cameras, the backdrop kinda gets wiped out slowly by the alpha plain. Like in Nanoid it's just a plain with a background texture, then that's alpha faded and the backdrop get's disabled so nothing gets wiped out, so if there's nothing on the screen but the background plain, it'll look like it's just a backdrop texture - but when you put anything on the screen (even text) the backdrop keeps it there and fades it out because the alpha plain slowly overwrites the backdrop. With moving objects you get trails and stuff, but it can really help exagerate particles and stuff too, because they stick around longer, therefor you need less to get a good effect. It also neatens up particle deaths too, like if you suddenly remove an object, it'll be more like it fades out because it'll leave it's backdrop legacy behind.
I think Yusaku was the first person to do this, back in DBC, he used a ghosted and negative ghosted plain - it's just so much nicer using alpha instead though, you can jiggle the alpha plain about with a texture on it to give some crazy effects.
Not sure if Echoes uses a bloom shader as well as that technique, I think it's all done with sprites so I'm not sure how it's so bright and colourful.