It's not a matter of being more productive, it's a matter of doing work that matters more.
Twitter alerts to my cell phone that feed from Google calendar make me more productive. I can use Zapier or IFTTT to trigger tweets 15 minutes before an appointment.
The twitter account I use is private, so it's not viewable by others.
Here are some creative ways to use twitter to be more productive by working on what matters more!
As a timekeeper: You tweet at the start of task and note the time you stop on a google sheet (which automatically populates tweets).
I prefer to use AuthorDock as an actual time logger since it has a start/stop. But I can link to a tweet if that helps.
https://login.authordock.com/issues/1200