Who has priority here?

[Amoeba]

It's easy, you have right of way for going through the traffic calming, not for any other maneuver. As you wouldn't be going through the traffic calming, the other guy wouldn't have to give way and could just drive on through and pass you sitting waiting to turn right (looking at the photo it looks as though somebody could still physically drive through and pass with a car in position to turn).

However I imagine if all this played out 'for real' he would let you turn before trying to get past. Manners and all that... .

 

[ng93]

I'm guessing the sign only applies to the traffic calming bit, and that the right turn should be treated as any other right turn i.e. it's not your right of way.

Although common courtesy says they'd let you through anyway.