When they have visions of scenes they have never seen in the flesh, memories of acts and events dating back in time, the simplest explanation is that they have lived before.
But they make the mistake of ignoring their own duality.

They do not recognize their other-personality.

They think it is their own personality, that they have only one personality; and from such a premise they can conclude only that they have lived previous lives.
But they are wrong.

It is not reincarnation.

I have visions of myself roaming through the forests of the Younger World; and yet it is not myself that I see but one that is only remotely a part of me, as my father and my grandfather are parts of me less remote.