To apply a master page, either drag the master page icon in the Pages panel and drop it onto the page icon, or right-click the page icon and choose "Apply Master to Page".
The problem is that you have master text frames on your master pages, which you don't need in this scenario, and in fact mess things up a bit. With the workflow you describe, you are ending up with TWO text frames: one from the secondary master page (empty) and a "real" one that's local to your page. This is one of those baffling conundrums: you don't realize you have an empty text frame under the text frame you can see.
In fact, you don't need master page text frames, and you don't need to thread anything on master pages.
Set up the margins where you want them for your A master, create your B master based on it, with its different margins.
Place your manuscript document into your first spread. With the Place cursor loaded, hold down Shift and click in the top left corner of the frame created by the page margins. (You will see the cursor change from black to transparent, and an "down up over and down" icon to indicate the autoflow. This creates the pages and autoflows the text into recto and verso on each spread automatically.
From the Layout menu, choose Layout Adjustment. Turn on the "Enable Layout Adjustment" checkbox.
Drag the B master icon onto each of your chapter opener page icons. The text frame margin will automagically adjust to the settings from the B master.
As an added benefit, if you later decide that you want to tweak the margins, you can change them on the master page and the text frames will all adjust to the new setting. (NOTE: Any objects that are not in close proximity to a margin or guide will NOT adjust. Read over the settings in the Layout Adjustment dialog for more on this.)