At the end of each initiative pass, subtract 10 from each character's initiative score. Characters with a score higher than 0 get to go again during a second Initiative Pass. This process is repeated until all characters have an Initiative Score of 0 or less, the Combat Turn ends, or the combat ends.
There isn't some action that swaps a user from using the Matrix vs not using the Matrix.
There is no reason for it to exist. You do not switch to AR, you are always in AR. The difference now is that you have additional initiative that only applies to AR, not physical, rather than being indivisibly both. If there was truly no difference between the two, they wouldn't even need to specify AR as an initiative type.
The books would mention this.
Page 229.
Faces, mages, street samurai, all getting an extra +1d6.
Sorry, now you're just being silly and conflating AR initiative with physical initiative. Under which circumstances are any of those going to prefer +1d6
matrix initiative over, say, an agent that can do matrix activities for them?