The role of combined fluctuations in the input and output flows is analyzed on a model for explosive kinetics presenting reactive intermediates. In the deterministic limit the system is an extension of other kinetic schemes extensively studied which have third-order autocatalytic elementary steps. However, it represents a more realistic situation since it does not involve such low-probability third-order collision processes. It has an additional fast-relaxing degree of freedom: the concentration of an intermediate species. The multiplicative noise in the evolution of the fast variable corresponds to the fluctuations in the input flow. Only if these fluctuations are neglected in the adiabatic elimination limit, our model yields the results as obtained with previous models. However, applying the center manifold techniques, we show that these fluctuations are crucial since they can reinforce or inhibit the explosive tunneling effect caused by the noise in the output flow rate.