The Internet Archive discovers and captures web pages through many different web crawls.
At any given time several distinct crawls are running, some for months, and some every day or longer.
View the web archive through the Wayback Machine.
Content crawled via the Wayback Machine Live Proxy mostly by the Save Page Now feature on web.archive.org.
Liveweb proxy is a component of Internet Archive’s wayback machine project. The liveweb proxy captures the content of a web page in real time, archives it into a ARC or WARC file and returns the ARC/WARC record back to the wayback machine to process. The recorded ARC/WARC file becomes part of the wayback machine in due course of time.
TIMESTAMPS
The Wayback Machine - https://web.archive.org/web/20160403101603/https://support.twitter.com/articles/66884
After you protect your Tweets, only you and your followers can read your updates or see your Tweets in Twitter search.
If you at one time had public Tweets (before protecting your Tweets), those Tweets will no longer be public or appear in public Twitter search results. However, unprotecting your Tweets will cause any previously protected Tweets to be made public.
To find out how to remove your updates from Google search, check out this article. Twitter does not have the ability to remove content on websites other than twitter.com.
What If my Tweets have never been public?
If your Tweets have never been public (in other words, you've always had your Tweets protected in your settings), your updates should never show up in Twitter search or other public search engines.