No the league is not going to be the complete difference in moving across leagues but working with Rothschild definitely could have been the reason. It has been documented that he has been able to increase players K/9 over their seasons, and last year was no different for Silva.
There is something definitely odd about Silva's numbers, but his xFIP wasn't all that crazy last year. He put up a 3.9 for the season which sure is a bit low, but his career is at a 4.43. You figure that a change in league probably drops that down by .25 or so, and its not all that far out of the norm. A 4.2 is definitely within the margin of error, and can be attributed to him actually being healthy for the first time in years as well as changing leagues. Not to mention working with one of the best pitching coaches in the business.
What I find significantly amazing this year are his projections. The fans project him at a 4.08 FIP, and Tango with him at a 4.15 but yet they project his ERA to be 4.70 and 4.73 respectively. Which doesn't make a whole lot of sense.
If Silva is healthy then he can truly be the pitcher that he was from 2004-2007 with the Twins, and his 2010 wasn't all that far off from those.
So I think you can consider 2006, 2008 and 2009 to the outliers, not the other way around. Silva IMO is an above average major league pitcher. I am not sure if Cashner is.