No, no, that is not what is supposed to happen. I remembered it correctly: Yes, it's correct that you cannot be a champion without being exalted, but you can get the quests in the faction's tent with the faction you want to work on. You don't need ambassador to have the quest.
It is confirmed on Warmane's own guide. Point 6:
"6. You are now a champion of your race's city. You should move on and get more titles. Next step is going at the other npc that offers you the same quests as Eressea Dawnsinger, but for another city. Do steps 4 to 5.3. (including). " (It's here:
http://forum.warmane.com/showthread.php?t=31004)
So I guess it is a bug.
Thanks for your answer.
Regards,
Scorpyo