Hydrogen spillover is important in solid-phase catalytic hydrogenation reactions, as well as in hydrogen storage and scavenging. The present study explores the nature of this phenomenon by examining the effects of hydrogen pressure and addition of carbonaceous additives, such as carbon nanotubes (CNT) and C60 fullerene, on hydrogenation reaction kinetics and its products distribution. For these purposes, a solid-phase hydrogenation reaction was studied, where 1,4-bis-(phenyl-ethynyl)benzene (PEB) was used as a hydrogen acceptor. To the best of our knowledge, this is the first study in which both the reaction kinetics and products distribution of the solid-phase organic hydrogen acceptor were analyzed. A demonstration of hydrogen spillover phenomenon was provided on the basis of the combined interpretation of kinetics and hydrogenated organic products distribution, under different reaction conditions. The results were explained in terms of hydrogen active species availability, distribution and relative migration distance of these species through the carbonaceous media. The insights into the hydrogen spillover chemistry obtained in this research allow for a better understanding of this phenomenon and its implementation in the future hydrogen storage and transportation, and hydrogen-generating devices, including safety aspects of all these applications.