It seems clear we are not going to get any assistance here in this forum.
I think with everything that is going on, it's now more important than ever to keep an eye on these notifications to check where they are coming from.
If you get one, don't ignore it.
First, check that it is a legitimate email. It should contain a button / link "Review recent activity" that should link to
https://account.live.com/activity (if it goes somewhere else don't click the link!). If you're not sure, just go to the above link directly.
Sign in to your account and check the recent activity. I'm in the UK, so what I see that is immediately odd is logins from the United States. If you open any of these records it will show the IP address of the request along with other details. If it was
you, then it show your external IP address (which may be static or one that belongs to your ISP depending on how you are connected). You can see your current external IP address easily by going to a site like
http://whatsmyipaddress.org/
If the IP address isn't one you recognise then open up a Google search page and paste the IP address into the search box and search for it. You will see a bunch of results that are mostly IP address information databases or lookup tools.
In my case, all of those USA ones are from Redmond, Washington - you know who's there, right? All of the activity that is not mine belongs here, which are Microsoft servers.
HOWEVER, don't start ignoring these emails, because you could end up in a "boy who cried wolf" situation and may well miss one that actually IS a real breach and not one of these false alarms (as confirmed in my case by Microsoft).
DO turn on two-step / multifactor authentication on your account. Go to https://account.live.com, login, go to Security & password, tap Turn on two-step verification.
I do hope Microsoft will address this issue. I have tried contacting them directly as suggested. The first response was basically "everything is fine - don't worry about it". I pursued them for more detail but so far have been ignored with no further
response.