Hm.. still not sure, but there are some possibilities. In my opinion Ciel did not really come back to live as human, more like a bizzare doll that undertaker had been working on, but maybe this time undertaker really did succeed(since from the atlantic arc he mentioned that he wanted to experiment if human can be brought back to life and their life record is redesigned)
Ever thought that maybe undertaker told lizzie he can bring back the real ciel (her true fiance) and all he need was her blood (since on the previous chapters we found out that lizzie had a very rare star or blood? Sry i forgot) and maybe that's the ingredient that Undertaker never had to complete his bizzare dolls? and that's why lizzie told sebastian she can not return home yet?
o0o !
Maybe everything about him is intact but the soul. I don't know what this would mean within the context of the manga, but I assume reviving the body would revive the brain so all the memories would remain. So even without the soul, if he was properly reanimated by the undertaker...it seems plausible.
Sebastian ate Ciel's soul and he said the consumed souls don't go anywhere so maybe during the Atlantic arc when Grell cut Sebastian Ciel's soul escaped? Then Undertaker could easily bring back him to life