When you purchase a book using your web browser, you must select which device or app you want Amazon to send the book to. When you purchase through the Kindle itself, the book automatically is delivered to that device.
All other devices must explicitly download the book from the "cloud" storage at Amazon.
Or, you can navigate to the "Manage my devices and content" on the Amazon web site (under "My Account") and select the "send to ..." action to send the book to a given device.
I know of no way that any Kindle or app will automatically download all books from the Kindle cloud storage.
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