How did Aharon and his sons know when they were going to travel?
Rashi and Seforno: They knew that they were about to travel when the Pillar of Cloud gathered above the Camp of Yehudah. 1
Rashi (10:17): The moment Yehudah began to travel, Aharon and his sons entered the Mishkan and took down the Paroches and covered the Aron with it 2 (and also the other holy vessels, as the Pasuk goes on relate).
Rashbam: "bi'Neso'a ha'Machaneh" means whilst the first two camps 3 were traveling.
See also Seforno.
Rashi (ibid.): As the Torah writes here "And Aharon and his sons shall come ... ". The Bnei Gershon and Bnei Merari then came and dismantled the Mishkan and loaded it on to the wagons, and the Aron and the Holy vessels, which the Bnei Kehas would carry, remained standing covered, in their place, attached to poles, until Degel Machaneh Reuven traveled, at which point the Bnei Kehas traveled (carrying the holy vessels on their shoulders).
Degek Machaneh Yehudah and Degel Machaneh Reuven.
Why was it necessary for Aharon and his sons to cover the holy vessels in advance? Why could the Bnei Kehas not do it when they came to carry them?
Rashi (on Pasuk 15): To avoid the Bnei Kehas dying at the Hand of Hashem, by inadvertently touching the holy vessels, as the Torah indicates in Pasuk 18, 19.
Torah Temimah (on Pasuk 18, citing the Yerushalmi in Bikurim, 2:1): To avoid the Bnei Kehas dying at the Hand of Hashem by deriving pleasure from gazing at the Kodesh Kodshim.