No they don't. All they show is a 9% increase in arrests. The direct relationship between the two approaches zero.
Immigrants come to the USA to work and work mainly in the construction trade and some in the tourism trade.
No construction means no immigration.
The decline from 2005 to 2011 is likely a decline in construction and tourism.
The recent uptick in housing in 2012 is probably the cause for more immigration and more arrests.