That's not to say anything for or against the program, but I think that they are overstating things.
If you want a chart that shows a 'possible driver' of lowered poverty that lines up a little bit more nicely with that graph, try this [1] which is just US BLS unemployment. As millions of people become unemployed ... child poverty rates spike, as they become employed, they go down.
[1] https://tradingeconomics.com/united-states/unemployment-rate