With the 'i' or 'ie' endings, those are more of a French variant, as European royals were fleuent in French, as it was the court language. This explains why many people who knew the IF and wrote about them called Anastasia "Anastasie".
As far as the Russian pronunciation, Svetabel ought to know, so you can trust what Svetabel has to say. But perhaps, being an English-speaker who is learning Russian, and the way things are pronounced, I might be able to help you...
Tatiana in Russian is pronounced more with the 'ti' being very short, if I am correct, and it would be "TA-ty'Ana" It's hard to write the sound, but hopefully you get what I mean. I don't know really how I ought to explain it...Anastasia has a more short sound on the 'si' and it's less of a 'z' sound I think. I may not be right with Anastasia's name, but I'm pretty sure on Tatiana's name.
Olga's name, if you're interested, is pronounced in Russian more like Ol-GA. The 'L' is very short, almost not even there, kind of like you're saying fast, and the G has a more pronounced sound.
Hope I was not incorrect in anything, and that I explained it well enough.