I believe you are right in the timing.
Starways Congress sent the order to the fleet, and Jane blocked ansible communication with the fleet in order to stop them from receiving the order.
It's important to note that Jane was fully aware that cutting off communication with the fleet would eventually result in her existence being revealed.
Starways Congress was fooled because, at the time, it simply was nearly inconceivable that anything would have the power to selectively interfere with ansible activity between multiple ships. Ansible communication was thought of as infallible, and the computer security used to protect and regulate it was regarded as equally infallible. As a result, other scenarios such as complete, simultaneous destruction of the fleet were likely considered first.
Eventually they did realize that the loss of communication with the fleet had to have been because of direct intervention by someone or something with the ability to track, monitor, and control all ansible communications. However, reaching this conclusion took the diligent and methodical analysis of one of the most brilliant minds in all of humanity: Han Qing-jao of the planet Path.
Without the artificially-enhanced intelligence of Han Qing-jao, it might have taken months, or even years, before anyone started speculating on direct access to the ansible signals, and even then they probably would have started with the idea of a computer virus, rather than a sentient artificial intelligence (in fact, I believe even Han Qing-jao assumed it was a virus at first), but they would probably have reached the correct conclusion eventually.