Modulating the interaction between the atoms in a Bose-Einstein condensate (BEC) can give raise to diverse phenomena depending on the frequency and amplitude of shaking. When the frequency of modulation is tuned close to collective mode resonance, Faraday waves appear. At low frequencies granulation of BEC is observed, whereas at high frequencies matter-wave jets are emitted. We demonstrate the emission of correlated atom jets from a matter-wave soliton in a quasi-one-dimensional optical trap. All stages of the jet emission are captured in a simple model based on the 1D Gross-Pitaevskii equation (GPE). Beyond the scope of the mean-field GPE simulation, the jet number correlations are investigated. We show sub-Poissonian statistics of the number difference between the left and right first-order jets in a regime of suppressed second-order jets.