It's not so much that the status of other jobs are reported when you start a new one, but that changes of status are by default only reported before a prompt is displayed. So in your case, it's reported at the first opportunity, that is at the prompt displayed after you start your second job.
You can make the job reporting synchronous by issuing:
In that case, reports on completion or suspension... of background jobs is done as soon as it happens and you don't have to wait for the next prompt.
If you don't want to be notified of the completion of a job, as @Scott says you can start it as a job of a subshell
(job &), or
disown it using the
disown command (or with zsh, start it as
job &!) but note that it means you can't put it back in foreground or kill it using a job number.