There are three routes: at the Thai mission covering you before you travel; arranged affixation on arrival at a named airport; or in Thailand at the Immigration Division in Bangkok. The programme's instruction sheet names Suvarnabhumi, Phuket and Chiang Mai only for the airport route, on a direct flight and arranged days in advance. It is not available at every airport, and an arrangement is not permission to enter.
For affixation in Bangkok, the passport must match the one on the membership application, and holders of some current visas are told to cancel them at the office that issued them first. Proof of where you currently are is proof of location — it is not permanent residence, and it is never recorded as such.
Two visa types appear for members: the Privilege Entry Visa (PE) and the Special Entry Visa (SE). Which applies to your package is not established by the sources we could read, so it stays a question for the programme or the issuing authority, and the answer is recorded as they confirmed it.