When convention doesn’t convey the proper flow of the conversation then you have to improvise. I’ve seen this in western comics before, though I don’t have any examples on hand. The bubbles have a tail indicator to show who is speaking and a flow indicator to show the order in which the bubbles are spoken. It is a little strange in this case but it’s not unheard of and it does the job it was drawn to do.

The connection between the bubbles guides you to the next bubble in order of dialogue. Without it it would read as if the man says everything first before the woman speaks which is incorrect.

It makes sense to me. You start in the top left like how you read and then you get a direction for the order of the conversation. I read it naturally at intended the first time through.