Am I obligated to offer expiation for an oath after I made my sister swear to wake me up after Fajr prayer, and she did not, and then I ordered my brother to wake me up?

An oath is based on intention. If your intention was for your sister to wake you up for Fajr prayer by any means, without a direct condition from her, then there is no expiation for you, as she fulfilled it; because the objective was to wake up for the prayer. If you had no specific intention, then the purpose was merely to be awakened. However, if you intended for her specifically to wake you up without any intermediary, then you have broken your oath by her not doing so, and expiation for breaking an oath becomes incumbent upon you.