This must be done on your first playthrough. In order to keep your underbosses alive, you must distribute the districts equally 3 for each underboss. If you give more districts to one underboss than the other, they will get resent you and they will walk out. You will then have no choice but to kill them.
When you are taking down a district, decide which underboss you are going to assign it to. You will need to assign each racket in the district to that underboss also because assigning rackets to one underboss and then giving the district to another will make them unhappy and could cause them to walk out. Make sure each underboss has 2 districts before you begin giving them a third district.
Distributing it rotationally with your underbosses should work.
However, if you want to distribute the racket according to their affinity you can check them below for suggestions.
(Format: Racket & Racket=District)
Cassandra: Garbage & Guns=Barclay Mills, Southern Union & PCP=Frisco Fields
Vito: Construction & Blackmail=Downtown, Sex & Drugs=French Ward
Burke: Auto Theft & Smuggling=Tickfaw Harbor, Gambling & Black Market=Southdowns
However, using either rotational or using their affinity will still unlock the trophy as long as you distribute the racket evenly. Since some rackets can give you better equipment.