I would say that the whole 1st claim/2nd claim thing is part of UKA's rule of competition. So it's only relevant to UKA licenced events.
Last time I looked ARC did not have any affiliations to higher sports instiitutions, and was not a competition provider so UKA affiliation (or not) would be irrelavant.
UKA/EA/Power of10 do not acknowledge any ARC events and results etc are not listed.
The first UKA registered club that you join will become your 1st claim club, although you can change it later. After that you can join as many clubs as you want.