Alright, the Puppetmasters are their OWN organization, they work to profit themselves. They are competitive against people like Aria and work to take profit away from them and into their pocket. The Client actually used to be one of them, but something happened and the rest of the group cut him off. He is seeking revenge and using as many resources as possible to take them out. Aria wouldn't mind taking out some competition now that she's realized these Puppetmasters exist. They don't make the criminal world tick, they just take a slice of profit from everything. 

I didn't to tell you this because, plot development, but since you needed to know, yeah. You don't know the Client is an ex-Puppetmaster and that he just wants to take over the criminal game again.