I would have used on of these to set my base on, http://www.strongtie.com/products/connectors/ABW.asp
With the post being indirect contact with the concrete in the Sonotube it can wick up moisture and rot out the post.
I would have avoided butting two rim joist, at a post. Instead there should have been one soild one and the other one could have been butted. With two joining there you will have made a pivit point where the rim can sag or bounce on each side of the post.
All an inspector is going to be looking for is the bare min. that code calls for.
By using 6 X 6's you would have had far more bearing suface to suppot the rim joist and not split out when bolted.
For any joist run over 6' I would have gone with 2 X 8's for joist and 2 X 10's for rim joist.