Helium nanodroplet isolation is used to produce van der Waals-bound quartet state alkali trimers (Na-3 and K-3) selectively over the corresponding chemically bound doublet trimers. Frequency-resolved excitation and emission spectroscopy reveals the presence of nonadiabatic spin-flip processes in the electronically excited states. A total of four quartet to quartet electronic transitions are observed: the 2 E-4('),1 E-4<--1 (4)A(2)(') transitions of Na-3 and the 1 (4)A(1)('),2 E-4(')<--1 (4)A(2)(') transitions of K-3. Time-resolved spectroscopy reveals that intersystem crossing times in Na-3 decrease from 1.4 ns after excitation of the 0-0 band to approximately 400 ps for the higher vibronic levels (3,5/2). Analysis of the resonant quartet fluorescence reveals that the excited electronic state cools vibrationally on a time scale that is comparable to, but slower than, the intersystem crossing time.