I don’t know what the exact parameters are, but Google does indeed check certain websites at certain times – when it’s most likely a new post will be published. I haven’t seen this on sites where people only post a few times a month but for sites that publish daily, I’ve seen it happen quite a bit. My website gets hit by the Googlebot at least 3 times a day, which I’ve verified, and sometimes the post will appear with a “site:” query within 5 minutes. Please note that because it appears in the results, it doesn’t mean it’s fully indexed. Usually when you see it for the first time, either the meta description (if you have one) or the first 150 characters of the post will appear as the snippet.