According to Massie, and the books of those who knew Alix well (Vyrubova, Buxhoevedon, Dehn, Gilliard) her main language was English. It's common and well accepted knowledge that this was true, and that she and Nicky spoke English to each other. Her letters and diaries are English, and she spoke mostly English with the children. As has been mentioned by others, the children learned English young and had some British nannies. No one is saying that Alix didn't speak German, I'm sure she did. She spoke it to her father. However, English was clearly her language of choice. It should tell you something that her correspondence with her siblings, also half German, was in English. They were raised by British nannies, and after their mother died, spent a great deal of time in England with Grandmama Queen Victoria. English was the most used language in her family growing up, and since it was her best language, it became used very much among her own family (Nicky and the kids) Those who were close to Alix described her as having the ways of a Victorian Englishwoman. No one who knew Alix in real life ever said anything about her using German with any frequency, if at all.
On the subject of the guards saying she spoke German, I agree with the poster who said that the guards likely didn't know the difference. Most of the people who became Bolsheviks were peasants, mostly uneducated, many illiterate, few if any had been exposed to foreign languages. Because of all the rumors about Alix being a German spy, being called The German Woman by her enemies, naturally they would assume any language she spoke other than Russian must have been German, but that doesn't mean it was. In The File On the Tsar it says that the Bolsheviks forbid the family to speak any language other than Russian, so that they could be understood. Summers and Mangold wrote that the family was forbidden to use their usual English.