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We showed in previous work that for Yang-Baxter (YB) deformations of AdS$_5\times$S$^5$, the open string metric and coupling, and as a result the closed string density $e^{-2 \Phi} \sqrt{g}$, remains undeformed. In this work we identify the Page forms as the open string counterpart for RR fields and demonstrate case by case that the non-zero Page forms remain invariant under YB deformations. We show that these results remain true, not only for homogenous YB deformations, but also for modified YB deformations associated with $\eta$-deformations. We give a physical meaning to the Killing vector $I$ of generalized supergravity and show for all YB deformations: 1) $I$ appears as a current for center of mass motion on the worldvolume of a D-branes probing the background, 2) $I$ is equal to the divergence of the noncommutativity parameter, 3) $I$ exhibits ``holographic'' behavior, where the radial component of $I$ vanishes at the AdS boundary, and 4) in pure spinor formalism $I$ is related to a certain state in the BRST cohomology.
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