Let (X2k, F, g) be an almost anti-paraHermitian manifold with an almost paracomplex structure F and a Riemannian metric g and let TX be its tangent bundle with the ciconia metric g˜. The purpose of this paper is divided into two folds. The first one is to examine the curvature properties of the tangent bundle TX with the ciconia metric g˜. The second one is to study conformal vector fields and almost Ricci and Yamabe solitons on the tangent bundle TX according to the ciconia metric g˜.