I think Twitter is a bit faster than that. Twitter users in Japan seem to respond really fast when they feel any moderate level of shaking; at times, if you follow enough Japanese people on Twitter, your entire timeline gets filled with people saying "oh hey, something's shaking" or "it's rocking" or "boobs!". So yes, you will get advanced warning if there are people closer to the epicentre than you posting on Twitter (and as long as they are not using a certain phone provider which got overloaded during the big earthquake/tsunami last year while all the other providers were fine).
I really can't believe that the reacting, tweeting, flagging, aggregating and alerting could happen in 20 seconds or less. Not a chance.
I find it extremely unlikely that tweets you're referring to were posted within 1/3 of a minute of the first shaking taking place.
Not to mention, that all of that aside, you still need a representative sample of people from a geographic area with public Twitter accounts. Unless you're OK with 8 people from the Salton Sea triggering an automated alert chain all the way to Santa Barbara. And you have to make sure no IP spoofing is going on to trigger a fake alert.
And then you have to make sure they're not dummy accounts. I don't have to tell you Twitter is absolutely filled with them.
"Sorry 3.8 million residents of L.A. who are without hot water / ability to cook until SoCal gas can come out and reopen all of your valves - a few people nonexistent people tweeted about an earthquake."
And then you still have no way to quantify the intensity of the shaking. A 5.5 is the same as a 7.2 in the minds of a Twitter user watching things fall from their shelves during the first 20 seconds of a quake.
If you don't have a rough approximation of how intense the quake is, you have no way to select the appropriate response.
This whole concept screams of another "WOW WEB 2.0 CROWDSOURCED USER CREATED CONTENT NONTRADITIONAL MEDIA" thing that moves forward based on the inertia of its own perceived specialness.