We study the four-dimensional relationships between magnetic activity, rotation, mass, and age for solar-type stars in the age range 5-25Myr. This is the late-pre-main-sequence (l-PMS) evolutionary phase when rapid changes in a star's interior may lead to changes in the magnetic dynamo mechanisms. We carefully derive rotational periods and spot sizes for 471 members of several l-PMS open clusters using photometric light curves from the Zwicky Transient Facility. Magnetic activity was measured in our previous Chandra-based study, and additional rotational data were obtained from other work. Several results emerge. Mass-dependent evolution of rotation through the l-PMS phase agrees with astrophysical models of stellar angular momentum changes, although the data suggest a subpopulation of stars with slower initial rotations than commonly assumed. There is a hint of the onset of unsaturated tachoclinal dependency of X-ray activity on rotation, as reported by Argiroffi+ (2016, J/A+A/589/A113), but this result is not confidently confirmed. Both X-ray luminosity and starspot area decrease approximately as t^-1^ for solar-mass stars, suggesting that spot magnetic fields are roughly constant and l-PMS stars follow the universal solar-scaling law between the X-ray luminosity and surface magnetic flux. Assuming convective dynamos are dominant, theoretical magnetic fluxes fail to reveal the universal law for l-PMS stars that enter late Henyey tracks. Altogether we emerge with a few lines of evidence suggesting that the transition from the turbulent to solar-type dynamo occurs at the later stages of l-PMS evolution as stars approach the zero-age main sequence.