The best way I can explain how to do a similar effect is to explain how all the emitters work in my example.
The two emitters named "blocker" are simple squares that have had their Size Y graphs animated so that they shrink down to nothing and uncover the underying background image gradually.
"Riser" and "Faller" are two emitters that simply sprinkle from offscreen to give the illusion that dust is coming down to form the logo.
The "sprinkles" emitters are line emitters with Get Transparency from Layer turned on, and their position has been animated to follow along the edge of the "blocker" emitters. Get Transparency causes them to only appear where the alpha channel of the background image is white, so in this case they appear only where the star is. The sprinkles are what gives the impression that the Riser and Faller particles are filling up the background image.