Yes, some specific tire brands do have a star picture on the sidewall (e.g. Michelin Diamaris for the 19", or the Michelin Energy MXV4 for the 18").
That simply means these brands were approved by BMW to go OEM on the vehicle at the time of the sale. It does not mean they are the only tire brand suitable for the vehicle. For example, I just got 19"rims with the Michelin Latitude Touring HPs, which do not have the star symbol, because as my S.A. explained they are V-rated All-Seasons, and BMW only approves H-rating for All-Seasons. Irregardless, they are still great tires.

In your case, if you have the OEM 19" sport wheels, then you have the staggered setup: 19 X9 rims on the front, and 19x10 on the rear. And if you're going for the Michelin Diamaris, there's really only one configuration of 255s on the front and 285s on the rear that are out there, whether you get them at the stealer or at the tire shop. And unlike my Latitudes, the Diamaris ARE BMW-approved, so you should see the star picture on each of the sidewalls. If you do not see the star picture at the tire shop then it's not the legitimate Diamaris tires and you should be cautious about what they're trying to sell you.