The problem seems to be related to the Auto-correct and Auto-capitalization feature. If I turn either one off (Settings->General->Keyboard), I don't have the problem but when both are on, it comes back. It also seems to affect the first character that I type in the input field.
With both Auto features on, if I go to the login page of Twitter and type, say, a 'v' as the first character of the Username, a capital V is entered and the "V" pops up, but if I backspace, tap shift to go to lowercase and tap v again, the v does not pop up from the keyboard but it does show up in the username input field. I can reset things if I tap the Done button on the keyboard then tap in the username field to bring the keyboard back up. The problem is still there, but I can see it happen with a new letter if I want.
Try it and post what you find. You don't have to have a Twitter account to see it happen and I'd be interested to know if it's consistent.