I was checking over the requirements for the "Yearling" badge after I earned it on the main science fiction site. It says "active member for a year with at least 200 reputation. If someone has only 190 reputation when their anniversary comes up and then they achieve ten more reputation a year later, will they get the badge as soon as the reputation is earned, or have to wait for another year?
It doesn't have to be your anniversary for the Yearling badge to be awarded.
Based off this Meta FAQ (specifically this answer), when you meet the requirement for the Yearling badge, you will get it the next time the job runs that awards the badge. If you are eligible for multiple Yearling badges, then you will get one each time the process runs until you are caught up. The job runs either hourly or daily, but I'm not sure which.
You actually need 201 reputation to get the first Yearling badge, however. The exact requirement is "Have a reputation of at least (number of years since registration) × 200 + 1 (starting reputation)"
Also this comment confirms:
I have been an inactive member with 1 reputation for 2 years. I recently started participating and I received 2 Yearling badges this week: one when I exceeded 200 reputation, and the other when I exceeded 400.