Imhotep doesn't believe Evie to be the reincarnation of Anck-Su-Namun. In fact, Imhotep raised the mummy of Anck-Su-Namun using the Book of the Dead while Evie was still alive, so it's impossible for Evie to be the reincarnation of her. You are correct that he appears to have fixated on Evie, but it's because Evie resurrected him, and he appears to believe she is the perfect sacrifice to restore Anck-Su-Namun to her former glory.
EVELYN: In the necropolis, when I saw him, - alive,... walking, he called me Anck-su-namun. And then in Mister Burns' quarters he tried to kiss me.
CURATOR: It is because it was you who read from the Book. He has chosen you to be the human sacrifice needed to regenerate the body of Anck-su-namun.
(Mummy, The Script at IMSDb)
Also, a viewing of The Mummy only and not the sequel doesn't support the idea of reincarnation at all. We see spirits come up from and go back down into the waters in Hamunaptra, or, at the end, be taken away by the chariot. They can't both do that and be born again into other bodies.