I know the add-on causes the problem, but it causes a problem because XenForo currently doesn't handle massive amounts of simultaneous alerts elegantly. I'm running 1.2
How are you so sure its because XenForo currently doesn't handle massive amounts of simultaneous alerts elegantly?
The amount of people "following" the announcement forums on XenForo would presumably be very large, XenForo never encountered a problem. Many big boards use XenForo (huge, large boards), they never encounter any issue. So it points to it not necessarily being a issue with XenForo, there can be many many issues. It can be with your webhost, they can limit something causing timeouts. It can be another add-on conflicting and thus causing more issues, saying it is a fault on XenForo's end is fine if you have solid proof to back that up, but currently no one has complained about alerts not being handled gracefully.
Thus pointing the blame at XenForo is not the right thing to do because at the end of the issue this won't be XenForo's fault at all. Does the timeout generate any error in the error log, or any error on the front end? What is the message you get after the timeout/any error pops up? Those logs will help us reach the core of the issue.
I would also like to inform you that 1.2 adds options to watch forums and receive alerts, but the add-on extends that feature (to force alerts onto a certain usergroup), so at some part it is the add-on to blame not XenForo and its way of handling alerts. As far as I'm aware XenForo even makes use of the deferred system to handle mass alerts (not sure, did read about something though).
The best thing that will enable others to help you would be to post any error logs that occur, or ask the add-on developer to look into this issue (via giving access to your forums if required). Are you on a shared host, VPS or Dedicated? We need to find out why the timeout is exactly happening.