In Chrome (and a number of applications) the cursor won't jump to the next line until you enter a non-"whitespace" character (so spaces will never drop it down a line). If you observe after keying in enough spaces to move the cursor all the way to the right edge, typing any other character (a number, letter, or punctuation), you will drop down a line. This is simply the way chrome handles textareas, and is not configurable.

On an unrelated note, "^" is a caret.