The twelve Adityas of the Puranas are the only institutional position Vidhatri holds, and he holds it in one text and not the other. The Bhagavata Purana names him among the twelve, beside Dhatri, so that the pair enters the class together. The Vishnu Purana list of twelve keeps Dhatri and does not name Vidhatri at all, giving Amshu in his place. Ten of the twelve names are common to both, and Vidhatri is one of the four that differ, standing against Amshu the way Savitr in the same list stands against Parjanya.
His presence raises the number of pure abstractions in the group by one, which is worth noticing because it says something about what the class had become. The Rigvedic Adityas are sovereignty gods: contract, allotment, custom, the bonds that guilt incurs. The Puranic twelve are a solar calendar with a god to each month. A compiler filling twelve slots from that later position had every reason to reach for a name meaning the disposer, since a god who arranges is exactly what a year of ordered months wants at its head, and no reason at all to keep a weather god or an obscure Rigvedic name that meant a share.
The atlas holds Vidhatri because the lists that define the Aditya class name him, and a class published with only its agreed members is a misleading thing. It does not hold him as a settled member. The membership is recorded as claimed by one Purana, with the text that claims it named, which leaves the reader able to see the disagreement rather than inheriting somebody else's edit of it.