I believe it's been proven impossible to write a spam filter to distinguish useful LinkedIn email from spammy LinkedIn emails, since the spam filter would then be able to solve the halting problem.
I didn't get an email until after I logged into my account with the compromised password. Then it sent me an email and locked my account. Sort of odd way of dealing with the problem.
It was just a coincidence that you received the email after you logged into your account. Logging into your account didn't trigger the email to be sent.
Linkedin should probably be the one warning me about this, but I never heard of this before.
Edit: filtered as Spam, nevertheless they should have locked my account.