Transitions between the Zeeman substates of Cs 6(2)P1/2 and Rb 5(2)P1/2 atoms, induced in collisions with He atoms, have been investigated experimentally by methods of atomic fluorescence spectroscopy. The collision process has also been studied theoretically with time-dependent perturbation theory. Cs or Rb vapor contained in a quartz cell together with helium at low pressure was selectively excited by pulsed dye-laser radiation to the 2P(1/2,-1/2) Zeeman substate in a magnetic field ranging from 1.5 T to 7 T. The fluorescence spectrum, consisting of components emitted from the directly excited state and from the collisionally populated state, was resolved with a Fabry-Perot interferometer. Measurements of the relative intensities of the fluorescence components yielded the Zeeman mixing cross section for Cs-He and Rb-He collisions. It was found that the Cs 6(2)P1/2 cross section varied approximately as B2 in the range 0 < B < 0.76 T, showed a much weaker field dependence in the range from 0.76 T to 5 T, where it peaked, and declined slightly at B > 5 T. The Rb 5(2)P1/2 cross section did not exhibit any variation with B. A theoretical calculation of the Cs cross section carried out using time-dependent perturbation theory explains the magnetic-field enhancement in terms of the minute magnetic-field-induced mixing of the P1/2 and P3/2 states and the resulting breaking of time-reversal symmetry. The results of the calculation are in good agreement with the experimental results at fields in the range 0 < B < 5 T.