We use a factorization scheme, analogous to the one proposed for single inclusive forward hadron production in hadronic collisions, to regularize the soft gluon divergence present in the deep inelastic scattering (DIS) cross sections in the dipole picture at next-to-leading order (NLO). We show numerically that in this carefully constructed scheme it is possible to obtain meaningful results for the DIS cross sections at NLO, and so we are able to quantitatively study the recently derived NLO corrections to the DIS cross sections. We find that the NLO corrections can be significant and sensitive to the details of the factorization scheme used for the resummation of the large logarithms into the Balitsky-Kovchegov (BK) evolution equation. In the case of an approximative factorization scheme we observe a problematic behavior of the DIS cross sections similar to what has been seen with analogously factorized single inclusive cross sections in hadronic collisions.