To get your third yearling badge, you must: 

 - have been a member for at least 3 years
 - have at least 600 rep

For some people, they get the badge on their anniversary because they have more than 600 rep before the three year mark. For others, it takes a little longer. If you had 101 rep after 3 years 1 month, then suddenly earned 500 more rep in a matter of weeks, you would earn three yearling badges within days of each other as you crossed each 200-rep multiple.

It does not matter when your rep was earned or at what pace. No process tracks how much rep you earned each year, though you can figure it out using graphs and the league pages.