Well, tsarevitch just means "son of the tsar" in Russian. But the others come largely from titles subordinate to the crown that are given by courtesy.

The Dauphiné was once an independent county called Albon, located in what's now southeastern France. There is a very old story that the count of Albon used a dolphin as his family crest and that his descendants therefore took it on, changing the name of the province to the Dauphiné of Viennois (a city that was presumably the main stronghold of the region) and calling the count the Dauphin. However, this doesn't fit the timeline: the title change occurred around 1110, and the dolphin itself doesn't appear until about a century later. Regardless, what is actually documented is that the land was purchased for the French crown by Philippe VI (whose succession I discussed here), with the requirement that the title be given to the heir to the throne.

Likewise, Asturias was a remote region in Castile (formerly an independent Visigothic kingdom, which then became Léon, which was then absorbed into Castile through personal union). In the mid-14th century, there was unrest in the area which Alfonso XI attempted to ameliorate by persuading a lord who held much of the land - who had various titles, but whose name was Rodrigo Alvarez de Asturias - to adopt his (Alfonso's) illegitimate son, Enrique. After Alfonso's death, to cut a long and complicated story short, Castile was plunged into civil war between his legitimate and legitimate sons, and Enrique managed to become king. Enrique then gave Asturias to his own illegitimate son, Alfonso, but this Alfonso would eventually revolt under Enrique's successor, Juan I, and Juan confiscated his lands. He then conglomerated it into the Principality of Asturias and attached it to the position of the heir.

I do not know the origin of the concept of atheling in Early England, but the position of Prince of Wales came about in a very similar way to that of the Prince of Asturias. Norman England began trying to eat into and conquer Wales from almost 1066, and after two centuries of this, the Welsh managed to get the English to recognize the title "Prince of Wales" as the highest Welsh authority in 1267. Unfortunately, roughly a generation later, the English decisively beat the Welsh and killed the princes, and Edward I named his son, the future Edward II, Prince of Wales. As with the dauphin, there is a sort of folktale on the subject - that he tricked the Welsh, telling them that he'd give them a prince who didn't speak English (the implication being that he would be Welsh) and then revealing that it was his infant son who didn't speak anything at all yet - and it is likely untrue.

In all three of these cases, the title reflects the importance of the region being "given" to the heir. Both Asturias and Wales were troublesome, having long histories of independence before being forcibly taken over by other states, and being large and geographically far from the political centers of their rulers. Dauphiné was not troublesome in this way, but it was large and important (and far from Paris). Making them the most important titles below kingship was a way of recognizing their significance, which would hopefully make them less likely to rebel, as well as elevating the heir to the throne and making him to some degree responsible for dealing with these regions.