To me it sounds like a nice gesture that just turned awkward, as some things do in life. No need to apologize or draw more attention to it. He could have been more gracious in accepting the gift but it seems like he was taken aback. Since you obviously picked up the cupcake and balloon at the last minute after going out, maybe he thought the attention on him was too much--for St. Patrick's Day you could have been giving a scratch-off ticket to all
of your clients as you visited them, so no one was singled out and that's why he was okay with it. Maybe he doesn't realize that you like to give extra gifts for personal occasions, or that you do it for all
You are right though, if he was uncomfortable with the attention, he definitely shouldn't have mentioned his birthday a second
Personally I don't always mention when it's my birthday, because I don't want someone to think
I'm fishing for attention. The most I usually do for other people is say warmly, "Oh, happy birthday!" because when it's sincere I think it makes people feel good; and that's the most *I* would want. But, I've had other people react to my casual birthday mention in weird ways--like, suddenly they feel obligated to insist on taking me out to lunch (and you can tell they just feel obligated), or guilty that they didn't get me something, or enthusiastically take it as an excuse to make a fuss, or something like that. It's actually an interesting sociological experiment, I think, to mention to random people that it's your birthday and see what happens.
Maybe in two or three weeks you could casually mention that you get personal occasion gifts for other clients all the time. Like, "Oh, those flowers are beautiful, they remind me of the ones I got for Other Client's housewarming a couple months ago." In some contexts that might seem braggy, but it this case it might point out to him that you do this kind of thing all the time, and mean it well.
One more thought: Some people see birthday gifts as a reciprocal thing, because everybody has a birthday. So when you did something special for his
birthday, maybe his first thought was, "Crud, now I have to figure out when her
birthday is and remember to do something for it!"