adiyen believe Dr Venkatesh must have mentioned this with some pramanam. Since, the difference is based on ‘kalai’, it is possible that it would be based on purvacharyars work. This is one of the difference in philosophy between the ‘kalai’.
[As an information :: adiyen enquired about “determination of type of mukti” in this forum. Velukkudi swamy replied that “No discrimination. Everyone would enjoy all glories”
Ref ::https://www.kinchit.org/dharma-sandeha/thread/determination-of-type-of-mukti/
His statement indicates about enjoying glories. Your query is about variation in different duties assigned to different Muktas.]
I only hope and believe Perumal will not be impartial with the inhabitanats of Vaikuntam. Probably, He assigns certain work to some selected Nityasuris / Mukthatmas ?. This could be the reason for mentioning variation in different duties assigned.