My TOC has three books with subtopics under each. However, it displays with the first subtopic in the first book open when I generate the help. I have tried everything I can think of to fix it including finding an answer here on the Forum (which did not work for me) and setting the startup topic to the desired topic instead of index.htm. Still no luck. I've tested in IE and Chrome and it still doesn't work the way I want. I can get it to work fine in WebHelp.
I've attached images that show what's happening and what I'd like to have happen.
Desired TOC display, but with Services topic showing, not Add a Group to a Client's Service.
Open the properties for the Responsive layout.
In the General section, ensure the start topic is named index.htm (sounds like you changed that)
Now click the Content section and nominate the desired topic.
I'm a little fuzzy as to what you're looking for & at what point. You want the help to launch to a specific topic with the TOC opened and synched to the topic displayed? Your first screenshot seems to indicate a Context Sensitive Help (CSH) call to a specific topic (which normally doesn't show the TOC and other items (index, glossary, etc.) visible) - is that what you're doing? Or are you expecting to launch the index page and then navigate to a specific topic?