Anakin had hoped Ashoka would return to the order before Order 66, so he could have intended Rex to become her right hand man. Alternatively, this could be a situation not unlike that of Commanders Ponds and Neyo of the 91st, with one assigned to Mace Windu, and the other Stass Allie. As AnakinВ’s right hand man, Rex would still have been the de-facto commander of the 501st Legion if he wasnВ’t presumed dead at the end of the episode, and Appo was likely a Lieutenant or Captain during the Jedi Temple Raid, and promoted to Commander after the fact.

The 332nd is still a division of the 501st though.

That and the tragedy of the 332nd Company would be too painful for him to bring up anyways, which is why he introduces himself as being from the 501st instead of the 332nd. So technically, he was back to being Captain Rex. In this episode, before Jesse attempts to execute him for 'treason' against the Grand Army of the Republic, he demotes Rex of his position as commander and Rex jokes he didn't like to be commander to begin with.

In Rebels, Rex introduces himself as Captain Rex despite the fact in the last days of the Clone Wars, he was Commander Rex.Of course Ahsoka is going to struggle getting away from him, Jesse helped capture Krell using different tactics.

They had to deal with rogue Jedi Pong Krell during the Battle of Umbara, with Rex and Jesse both there. The 501st employ tactics beyond 'shoot enemy until dead' like other regiments we see during Order 66, mainly because they are uniquely experienced in this fact.

Clone commanders and captains list