Season 5 Ep 11 of Person of Interest shows us that The Machine has been giving irrelevant numbers to others (Logan Pierce, Harper Rose, Joey Durban) for some time now.
Fusco was surprised, however Reese wasn't, or he didn't show it. He was cool with it. Considering that in previous episodes, he and Finch didn't want to include others into the group or recruit more members, knowing that the more people know about The Machine the more they will be targeted.
Keeping that aside, So now Pierce, Rose and Durban know about The Machine and are an assets now.
Prior to this episode Jeff Blackwell was recruited, I assumed it was by The Machine, since the recruiter had used the same recruitment speech Finch used when he was recruiting Reese. Root thought Blackwell was a Samaritan asset. Considering that we are never shown how Samaritan recruits its assets, we see a lot of Samaritan assets trying to kill Finch and his group. I am assuming that Blackwell is indeed the Machine's asset.
The question is, The Machine was in an open state while Root and Finch were repairing it. Did The Machine start actively recruiting more people during this time without Finch's knowledge?