I think you are taking this "order" way too seriously from a legal point of view. For one thing, the "amnesty proclamation" was an order from the President, not a law. The main impact was on property seizures. If you read Fleming (the source you cited), such as his various paragraphs on Federal property confiscation, you will see that anybody could (and did) have their property seized on all kinds of pretexts. Fleming gives examples like estates being seized from widows because their sons were soldiers in the war and so forth. After the war Alabama was not even a state, it was a military "district," and the soldiers just seized whatever property they wanted. Congress even passed a law explicitly stating that there was no legal civil government in the South. I do not know what caused Fleming to say that a judgement was made "on the basis of 1861", possibly some court case or other, but it would be a mistake to think that niceties like that stopped property seizures, or that it was consistently applied.
To answer your question more precisely: the main material effect of the "amnesty" was to influence property seizure and restoration. In courts, after the period of military occupation ended, some property owners tried to get their property back by suing. In all cases the deciding factor was whether the plaintiff was "loyal", the terms of the "amnesty proclamation" were a minor factor. How a particular court decided could vary completely from one place to another and one case to another.
As far as property seizures under the clause itself, it really depended on the prosecutor involved, not the state. For example, one of the most aggressive such prosecutors was John Underwood, a Federal judge, who tried to condemn and confiscate every single estate in his jurisdiction (Virginia) which in his opinion was worth more than $20,000. However, in the end none of these confiscations took place because the policy in Washington was "reconciliation", so his little project got abandoned.