"stopping to refill his cup when she did"

Consider the following sentence:

She got up to get some of the coffee he had made, stopping to refill his cup when she did.

What does the subordinate clause in this sentence mean? Does it mean when "she" has got coffee, she stops getting coffee and starts to refill "his" cup or some other meaning? But my interpretation seems a bit strange.

Stop here is used intransitively in a sense with which you may not be familiar. It is defined thus in Macmillan Dictionary, intransitive sense 3.c.

to pause while you are moving or doing something so that you can do something else
  He stopped and listened before opening the door.
  Did you ever stop to think what might happen?
  stop to do something: I stopped to get a drink of water.
  stop for: I stopped at the store for some cheese.

The operative sense here is that instanced at stop to do something.

That said, this is an awkward sentence.

• There are two gets in different senses: got up, to get coffee
• There are two infinitive phrases of purpose: to get ..., to refill ...
• It’s not clear what it is she stops: getting up will hardly do, so it has to be getting coffee , but that’s not something she is actually described as doing, only what she intends to do
• And stop isn’t a very happy use: does she really stop getting coffee to refill his cup, or does she also refill his cup while she’s at it?

I'd do it more like this:

She stood and poured herself a cup of the coffee he had made, refilling his cup as she did so.

Yes, it's clumsy. 'Get up' is not a continuous action, hence the continuous tense is not used. So, 'she' can hardly 'stop to refill his cup' in the middle of getting up. I'd suggest:

She got up and went to get some of the coffee he had made, and refilled his cup at the same time.

If the interruption is deemed to need emphasis:

She got up and went to get some of the coffee he had made. Realising he had finished his cup, she poured him a refill first.