To answer the op - it's a nuisance, but if you highlight the text you want to put into BBCode and then press the button, it will stay where you wish it.
It depends on the browser, but you may find that if you press return once or twice before pressing the BBCode button (so there is a return line after the last text) then you will probably be able to place the BBCode first and then type the text that you want.
Don't know why it has started doing it - I'm sure that it did not use to - maybe it will change with the next update...
AlmostEasy is right that other browsers are better to play TW on, it's just a question of whether you find it important enough to download another browser - if you're not constrained by a workplace policy, it is not difficult.