In the water war arc, you see pilots and standard white phase 2 clones, but Rex still has his original look (no helmet). In the two droid episodes, Wolfpack and the 91st Recon have their P2 armor, but the gunship pilots for Wolfpack didn't have their new helmets yet. You really first see a P2 armor in the S2 episode Senate Murders.
During the Clone Wars, the armorsmiths of Kamino [2] redesigned the Phase I clone trooper armor, creating the new and improved Phase II armor partway through the galactic conflict. [16] Field-tested by Advanced Recon Commandos, it quickly spread through the ranks of the Grand Army of the Republic, and was adopted by nearly all clones near the war's end. As with the earlier Phase I, clones.
The Phase 2 armor started with the beginning of Season 4 (at least for all clones). However, if it's a transition you are looking for.throughout Season 3, Arc Troopers were the ones that would test out Phase 1.5 helmets in preparation for Phase 2. I found this information by comparing the appearances list of the armor in Wookieepedia to the chronological list of the Clone Wars episodes.
Clone Cadets appears to be the first episode (in timeline) showing the Phase II clone armor, worn by Commander Colt of Rancor Battalion. The Clone Wars Episode 12 shows us why Captain Rex combined Phase 1 Clone Armor with Phase 2 armor, to create the most unique armor of any Clone Trooper in the Grand Army of the Republic. The first appearance of a phase 2 trooper (not counting ARC troopers) was in Season 4 Episode 1: Water War in a blink and you'll miss it scene.
Season 4 Episode 5: Mercy Mission was the first prominent appearance (and also was produced before Water War, so is technically their first appearance). Behind the scenes Phase II clone pilot armor first appeared in the the twenty-third chapter of Star Wars: Clone Wars. The helmet's appearance in Chapter 23 is different compared to its appearance in Star Wars: Episode III Revenge of the Sith.
In Clone Wars it appears enclosed, while in Revenge of the Sith the faces of the clones are shown. Is there any specific episode when the phase 2 armor was introduced or the transition was even referenced? From what I've watched they just seem to start wearing it starting around the umbara arc. Like, is there an episode about the transition or do you ever see rex welding his together etc.
Phase II Clone Trooper Armor was the commonly-used armor worn by clone troopers, after the start of the second half of the Clone Wars. The helmet design and body armor of Phase II armor differed greatly from those of Phase I armor. Regular Clone troops all wear Phase I armour in Seaons 1-3, before switching to Phase II in Water War, the first ep of Season 4 (besides some pilots who lag behind and don't get updated armour until later in the season for some reason).