I logged onto my google chrome account from my work computer and noticed the history from my personal computer as suggested thumbnails. I immediately closed out of chrome. Will this trigger a signal to the network administrator that I was accessing these web sites from my work pc?
Chrome recover your history, settings and data, such as bookmarks, extensions, etc., didn't access every site in history again, only makes a connection to Google Server to recover your Google Account. The same for using Chrome for Android or iOs.