The massive increase seen in the control group seems to indicate that either ~5% of the money delivers >50% of the benefit, or there were some other factors that were more significant than the money.
There are always going to be secular trends of surveyed people regardless of what they're given. First of all a lot of homelessness isn't permanent, so if you monitor a group of homeless people some of them will cease to be homeless over the course of time regardless of whether they're getting anything from you or even aware they're being monitored. And secondly people are aware they're being studied, and often react. That may be as simple and positive as doing more to help themselves because the nice person showed concern about where they'd be in six months time, but it may also be people acting or claiming to act differently because they believe the payments are linked to what they report (no matter how much surveyors insist it's unconditional and there's no judgement and no possibility of the experiment being stopped or continued...)