Premise: as stated before, "the" Ash in AoD is not the original Ash from TED and ED2. The Time-Space Vortex is not only a sort of mystical "nexus" connecting different worlds, dimensions, ages and spaces with each other: it also contains a "duplicating stream" strictly connected to the Book of the Dead and its apocryphal copies.
More specifically, the "new" Ash had been literally "built" from the original Ash's physical and psychical structure, but he wasn't an high fidelity reproduction anyway. The Duplicating Stream indeed "reconceptualized" the original Ash, and the final result features slightly different aspect and psyche.
For instance, there's no more the white streak, hair are a bit longer, skin is slightly tanned, a wrist watch the original Ash put in his pocket (he should have removed that before the gearing up scene in the workshed) has "appeared" again, the wounds are a bit different.
Speaking about personality and beahaviour, Ash II is more mentally unstable, volatile, prone to delirant egocentrism, and his past memories are a bit messed up and rearranged (the recap at the beginning of AoD).
Here things get confused a bit.
AoD has two endings.
1- The Post-Apocalyptic Damnation
Ash II drank 7 drops of mystical potion instead of 6. 1387 + 700 = 2087 A.D. This way, Ash II awoke in a post-apocalyptic London where bombs have been dropped in the past and maybe humanity is extincted. It is safe to assume he mispelt the preventive recitation ("Klatuu Verata Nicto") for the second time. Now we must clarify what's the purpose of it: the specific passage makes Ash undetectable to the Evil Dead. This would ensure he is not affected by the entity throughout his centennial sleep. Similarly, in the Cemetary the whole point of the recitation was to make Ash invisible to the Kandarian Demon when he is stealing the right Necronomicon Ex Mortis. We know it didn't work.
In this version, the S-Mart ending is just a dream Ash II had during his long sleep.
2- Return to civilization
Ash II drank a different version of the potion. He sleept and then succeeded into coming back to "his own time".
Ironically, his existence sprouted in the Time Vortex and was quantically finalized in 1387 A.D. His "present time" was just a memory tapped from the original Ash, an illusion.
The mystical serum must be different from the one involved into the Post-Apocalyptic ending, since his wounds don't regenerate during the big slumber.
He eventually finds himself located in 1987's England, presumibly few days (or even months) before the exact moment the original Ash has been sucked in the warp at the end of ED2; nobody could suspect or condamn Ash II for the gruesome events of the Elk Rapids Massacre, because evidence supports the fact he wasn't in America at the time.
Once come back in Michigan, he "retrieves" the original Ash's social and civilian life.
By this time, Ash II may be questioning his memories, but he cannot deduce he's a duplicate anyway.
Since he failed to spell the "Klatuu Verata Nicto" passage correctly (again), the Evil Dead detects him at the S-Mart store. We don't know why the Evil Dead is still active, maybe someone retrieved the tape recorder... the presence of the Kandarian Demon is problematic anyway.
In this version, the Post-Apocalyptic ending is just a dream Replicant Ash had during his long sleep.
30 years later...