"With the saints give rest, 0 Christ, to the soul of Thy servant where sickness and sorrow are no more, neither sighing, but life everlasting. "
These are the simple words to the Orthodox kontakion (hymn) for the dead. Regarding the story of the Imperial Family and this hymn at the Ipatiev House, it wasn't so much the words of the kontakion that were incredible... it was the circumstances!
The Liturgy at which this all happened was a Sunday Liturgy. Normally the Orthodox do not have requiems on Sundays, prefering to celebrate Sunday as the day of Resurrection. It was a "mistake" of the Deacon to begin singing this kontakion, and the priest just went along with it so as not to interrupt the flow of things. The Imperial Family went to their knees out of reverent custom.
Perhaps everyone in the room at the Liturgy that day had some level of understanding, conscious or subconscious, of the events about to take place there a couple of days later.