So he was turning right and overtaking someone else who was turning right while pedestrians were crossing the entrance to the road being turned into. This means that he was, apparently unaware of the pedestrians already crossing which might cause you to swing a little wide.

It would seem that he was not allowing a cyclist sufficient room to manouevre, by not allowing a reasonable space for right of way (I assume that cyclists are allowed some lateral space [3' ?] according to state law?). It would also seem that he assumed that you knew he was going to turn right at the same time that you were - again, is he allowed to do that in state law? To my mind, it would be an unreasonable demand to make of someone you are overtaking. In the UK, it is for the overtaking driver/rider to make sure that the road ahead of their direction of travel is clear.

On the basis of your description, the only minor criticism which any of us might make is that you might be a litle more aware of the possiblity of an overtaking car also turning right by engine sound/gear changing, etc. In his case it would seem that he was legally in the wrong, but you were, perhaps, slightly situationally less alert than might have been possible.