Once again, here's the link to J.K. Rowling's discussion of wands:
http://www.jkrowling.com/textonly/en/extrastuff_view.cfm?id=18
As she says, only Harry, Ron, and Hermione have wands which correspond to the Celtic calendar. As the rest of the characters' wands indicate, one's birthday does not necessarily determine which wand will "choose" you. Your birthday may be in July, but the Holly wand may not be the "right" wand for you. Look at JKR's description of why Hagrid's wand would be made of Oak. She has developed a lot of wand lore. The wand masters at Ollivander's aren't randomly "faking" it if they give you a wand which doesn't go with your birthday.