The order is browser specific and where feasible implemented using their native APIs. Hence, it's not possible to describe a single order for sending messages.
Additionally, the current appAPI.message.toAllTabs implementation does not provide a way to determine when the method has completed sending the messages, however, we are always interested in improving the experience for our users, and hence I have forwarded your suggestion on to our product team, who will consider it for future releases. Thank you for your input.
If you have a specific use-case and want to discuss it further in private, please feel free to email our support (support@crossrider.com).
[Disclaimer: I am a Crossrider employee]