The "naughty or nice" reference, whilst widely accepted as canon, is from "Santa Claus Is Comin' to Town", a Christmas song written by John Frederick Coots and Haven Gillespie and was first sung on Eddie Cantor's radio show in November 1934. The story of Rudolph was created by Robert L. May some years later in 1939 and was written as a poem in anapestic tetrameter before later being adapted into song by May's brother-in-law Johnny Marks in 1949 and is also widely accepted as canon but there is evidence to suggest that "Santa Claus Is Comin' to Town" and "Rudolph the Red Nose Reindeer" are stories in the same universe and that have been amalgamated by popular culture.
Haven Gillespie's inspiration for the lyrics was the recollection of his mother reminding each of her children that Santa not only knew when they were sleeping but also knew when they were good or bad so that idea does pre-date the song but the origins are unclear. It is apparent , however, that Mrs Gillespie employed the idea to willfully control and manipulate minors. The song itself implies that Santa Claus has the ability to observe every action and listen in on every conversation which effectively robs children of privacy and freedom and makes the song rather dark.
As well as being dark and Orwellian in nature, "Santa Claus Is Comin' to Town" does not anthropomorphise reindeer (or mention reindeer at all) whereas the original story of "Rudolph the Red Nose Reindeer" portrays reindeer living in houses and sleeping in beds and does mention that he "always knew which children were good" indicating that the "omniscience" that you are referring to regarding children exists in both stories. Neither story nor lyric provides evidence of Santa expressing sharp disapproval or criticism to anyone so there is no reason to question why he didn't rebuke the other reindeer. According to May's story in fact, all the reindeer who verbally abused Rudolph were his peers and were fast asleep when Santa visits the abode where Rudolph resides (in the story Rudolph isn't promoted, he is enlisted and is only awarded the title "COMMANDER-IN-CHIEF" on future dark trips). It is important so say that Santa's regular reindeer had no involvement in the abuse of Rudolph and there is no evidence to indicate that Dasher, Dancer, Prancer, Vixxen, Comet, Cupid, Donnen or Blitzen have ever been abusive or even unfriendly to Rudolph or anyone else for that matter.
As a further note, it is often the case that abuse is a learned behaviour and it could well have been the case that Rudolph's peers could have adopted the attitudes of their parents and elders when regarding an individual with a red and bulbous nose - a condition that was often attributed to drunkenness and alcoholism.
As evidenced by both songs and by the Rudolph story, one can conclude that the story does take place in a universe where Santa is "omniscient" and that his powers work on children of all species. However, Santa reserves the right act on his knowledge (or not to act) as he sees fit.
