Wondering how you setup your web alerts to know when a link is found to your site. If you use your domain name it will only find where your domain name appears in the text rather than all links where the anchor doesn't have the domain name. Am i missing something obvious?
But the problem is that link:yourdomain.com doesn't show anything accurate.
The site gets a link, Google crawls linking page and adjusts rankings of linked page - it takes days or in worst case weeks - and link: command often refuses to show this link FOREVER.
You cannot check your backlinks even manually, so notifying about getting them is totally impossible. Unless you use other SE than Google to check the backlinks, but other SEs may not know all links Google does.