Using the color dipole picture and the CGC effective theory, we investigate single inclusive jet production in DIS at small $x$ and relatively high $Q^2 \gg Q_s^2(x)$. We consider moderately hard jets, with transverse momenta $P_\perp$ within the range $Q^2 \gg P_\perp^2 \gtrsim Q_s^2(x)$, for which TMD factorisation is known to hold at leading order. We argue that the struck quark has a large virtuality $\sim Q^2$, that should be visible in the structure of the final state: the measured jet should propagate at larger angles, and also be much wider, than naively expected. We demonstrate that the next-to-leading order (NLO) corrections preserve TMD factorisation only for appropriate jet definitions, which account for the virtuality of the jet. We propose such a definition and show that the corresponding NLO corrections encode not only the JIMWLK evolution with decreasing $x$, but also the universal, DGLAP and Sudakov, evolutions of the quark TMD.
