Hi Anna,

ur guess is almost right, ~다가 is normally used when something happened while u were doing something 

for example,

I think I sprained my ankle playing soccer.

축구하다가 발목을 삐었나 봐.

She opened the sluices while talking on the phone.
전화통화를 하다가 그녀는 와락 감정을 터뜨렸다.

hope it helped