Swamy Namaskaram!
Yes, ParamAathma is inside of all Aathmas – Chith or Achith.
Hence, inside our body, for that matter, numerous Aathmas are existing. Aathmaas are not earning Kharmas; it is only the prakrithi sareeram that earns kharmas and clouding its associated Aathma.
These Aachits are not doing any Kharmas and destined to be in dormant state. Hence, during this state or period they are not earning either Pahbham or Punyam.

However, there is only one Aathma that is associated with the whole Prakrirhi Chith Sareeram ( say,of one person) that is entwined by the Kharmas earned by its associated Sareeram.

In summary, only one Aathma’s Ghana is impacted by the Sareeram it is residing.
Ofcourse, Bhaghawan is inside each and every Aathma in Antharyami form- be it Chith ot Achith.
Aathma’s Ghana have capability to have Bhaghavan’s Antharyami inside.

Hope, Adiyean can address your doubt from what is heard of Swamigal’s Divya Pravachanams.
Adiyean request you to listen to Swamigal’s pravachanams edpecially YMD and Dhasa Upanishads.

Adiyean Ramanuja Dhasan.

Bhramam resides inside each atma seperately as well as surrounds the whole vibhuthi. At the same time he exists as the smallest (antaryami) and largest around everywhere (sarvavyapakam)