Twitter is just a part of media like print / electronic or social media including Facebook; linkedin ; You Tube etc. And each type of report on any type of media has effect on the price of bitcoin. When there are positive news the price goes up and in case they spread negative news then the price falls.
I don't think that this is kind of true, its because even if the price goes upward, a lot of people in social media would likely to spread false news or articles about BTC and in that case I don't think that Twitter or any platform would likely to give a major EFFECT on the price of BTC, I just wish that more positivity would spread out in these social media platforms.