Alex Ivanov is absolutely right. That Russian teacher of yours would not be seen as русская in Russia. That Estonian girl may be seen as русская if she is ethnically Russian. A Uknranian will be украинец, not русский. Mind you, there may be an ethnic Russian coming from Ukraine - the opposite is also true -
we have украинцы who live in Russia (due to migration, etc.), but they aren't called русские. A Scotsman living in England will not be called an Englishman on account of his speaking English as his first language, likewise a Georgian will not be русский just because he speaks Russian fluently - he will be a грузин. He may be a Russian citizen, but he will never be Russian as русский - and he will not want to be called русский either.