As with most native A/B tests, the binary probably ships with code for both functionalities. When the browser launches for the first time they generate a random number, and if it's below a certain threshold you get variant A, above you get variant B. The information gets persisted on disk so it remains unchanged across sessions.
It seems that there is some communication back to Mozilla, since they claim that they can increase or decrease the number of users in each group over a week; that seems unlikely to come in the form of a new binary.
