Not sure why, but you are correct there were two blinker versions. Have yours already been installed? You should be able order the other versions. This link has more information with part numbers courtesy of BayernKiwiBMW in an old thread. I am not sure if the part numbers are all correct, but it should help you narrow things down.
The only other thing I can think of is if you have access to your old lights you should be able to swap the turn signal reflectors into the new headlights. Although given that you have a 2003 you may not be able to open them easily.
Your current ones look like these right?
Amber blinker w Amber corner (the blinker reflector is amber)
Your old ones looked like this right?
Clear blinker w Amber corner (blinker looks amber b/c of bulb & way pic was taken)
Close up of Clear blinker (ignore the fact that this is a clear corner euro version)
vs. Amber blinker
FYI there were 8 different combinations available 4 US versions and 4 Euro versions.
US DOT assemblies:
Halogen, clear blinker, lit amber corner
Halogen, amber blinker, lit amber corner
Xenon, clear blinker, lit amber corner
Xenon, amber blinker, lit amber corner:
Halogen, clear blinker, unlit clear corner:
Halogen, amber blinker, unlit amber corner:
Xenon, clear blinker, unlit clear corner:
Xenon, amber blinker, unlit amber corner: