Your understanding is right. We tend to use 'ga', when we want to emphasizes something.
I will give you an example.
When we want to say that it is me that drank the tea in Japanese, we will say ' 私がそのお茶を飲みました'.
In contrast, when we want to mention that I drank the tea in Japanese, we will say '私はそのお茶を飲みました'
I hope it will help your understanding.