The idea of Punk Eek is that the evolution takes place "off stage" where it isn't recorded in the fossil record so that when it later reappears there is a large change, an apparent saltation. The evolution that takes place "off stage" is assumed to follow normal Darwinian processes.
Using
Punctuated Equilibria as a reference
PE essential features are peripatric speciation in a geographically limited region and stratigraphically limited extent such that sampling of the fossil record will reveal a pattern of most species in stasis, with abrupt appearance of newly derived species being a consequence of ecological succession and dispersion.
While Eldredge and Gould acknowledge that geological processes contribute to the "gappiness" of the fossil record, they also assert that PE is by far the more important consideration in that regard.
Or in other words evolution takes place "off stage" where it isn't recorded in the fossil record so that when it later reappears there is a large change, an apparent saltation. The evolution that takes place "off stage" is assumed to follow normal Darwinian processes.