Rishonim definitely did not think of themselves as rishonim, as that is a relative term and no gadol would write something with the intent that later generations will NOT be able to argue on it.
I think it probably developed at some point due to the general writing style differences between the two groups; rishonim generally deal directly with the gemara’s shakla v’taria, and are generally much more terse and straightforward than achronim, while achronim often elaborate and focus on details in the gemora, bring up many tangential (albeit related) topics of halacha, and rarely argue with rishonim. I doubt any one individual decided, “I am (or Ploni is) the first acharon”. I think that at a certain point many of the gedolim just hesitated to argue with gedolim from previous generations, and at a certain point (possibly many years later) that hesitation was noticed and regarded as the “dividing line” between the two groups.