  A hybrid percolation transition (HPT) exhibits both discontinuity of the
order parameter and critical behavior at the transition point. Such dynamic
transitions can occur in two ways: by cluster pruning with suppression of loop
formation of cut links or by cluster merging with suppression of the creation
of large clusters. While the microscopic mechanism of the former is understood
in detail, a similar framework is missing for the latter. By studying two
distinct cluster merging models, we uncover the universal mechanism of the
features of HPT-s at a microscopic level. We find that these features occur in
three steps: (i) medium-sized clusters accumulate due to the suppression rule
hindering the growth of large clusters, (ii) those medium size clusters
eventually merge and a giant cluster increases rapidly, and (iii) the
suppression effect becomes obsolete and the kinetics is governed by the
Erd\H{o}s-R\'enyi type of dynamics. We show that during the second and third
period, the growth of the largest component must proceed in the form of a
Devil's staircase. We characterize the critical behavior by two sets of
exponents associated with the order parameter and cluster size distribution,
which are related to each other by a scaling relation. Extensive numerical
simulations are carried out to support the theory where a specific method is
applied for finite-size scaling analysis to enable handling the large
fluctuations of the transition point. Our results provide a unified theoretical
framework for the HPT.
