The first computation of Higgs production in association with three jets at NLO in QCD has recently been performed using the effective theory, where the top quark is treated as an infinitely heavy particle and integrated out. This approach is restricted to the regions in phase space where the typical scales are not larger than the top quark mass. Here we investigate this statement at a quantitative level by calculating the leading-order contributions to the production of a Standard Model Higgs boson in association with up to three jets taking full top-quark and bottom-quark mass dependence into account. We find that the transverse momentum of the hardest particle or jet plays a key role in the breakdown of the effective theory predictions, and that discrepancies can easily reach an order of magnitude for transverse momenta of about 1 TeV. The impact of bottom-quark loops is found to be visible in the small transverse momentum region, leading to corrections of up to 5 percent. We further study the impact of mass corrections when VBF selection cuts are applied and when the center-of-mass energy is increased to 100 TeV.