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A scalar superfield transformation is a pullback under a supertranslation. Since that transformation mixes $x$ and $\theta$, an odd-coordinate derivative acquires an extra spacetime-derivative term under the coordinate Jacobian. It therefore does not transform as a spinor superfield merely by differentiating the scalar transformation law. This is partial derivatives and superfield covariance.

For explicit signs, split the Majorana spinor coordinates into ${\theta }^{\alpha },{\bar{\theta }}^{\dot{\alpha }}$ and use left Grassmann derivatives. Choose the differential generatorsFor example, $\{{\partial }_{\alpha },{\bar{Q}}_{\dot{\beta }}\}=i{\sigma }_{\alpha \dot{\beta }}^m{\partial }_m$, which is nonzero. Commuting the even supersymmetry variation through ${\partial }_{\alpha }$ consequently gives the unwanted translation term.

Replace the ordinary odd-coordinate derivatives by the supersymmetric covariant derivativesThe graded product rule cancels the mixed coordinate/derivative terms, giving $\{D,Q\}=\{D,\bar{Q}\}=\{\bar{D},Q\}=\{\bar{D},\bar{Q}\}=0$. Thus $D_{\alpha }V$ and ${\bar{D}}_{\dot{\alpha }}V$ transform as spinor superfields. Their own mixed algebra is $\{D_{\alpha },{\bar{D}}_{\dot{\beta }}\}=-2i{\sigma }_{\alpha \dot{\beta }}^m{\partial }_m$, with equal-chirality anticommutators zero. This covariant differentiation is also what makes a chiral superfield constraint ${\bar{D}}_{\dot{\alpha }}Z=0$ supersymmetry invariant. Negating every barred derivative is another convention, but changes the displayed mixed-algebra sign.