We present the first experimental study of time-resolved fluorescence from laser-excited Cs(6P(1/2)) atoms isolated in a solid He-4 matrix. The results are compared to the predictions of the bubble model including the interaction of the atomic dipole with its radiation reflected at the bubble interface. Our results show that in liquid He as well as in the body-centered cubic (bcc) crystalline phase of He the lifetime of excited Cs atoms does not depend on He pressure, in agreement with our theory. When going from the bcc to the hexagonally close-packed (hcp) phase of He-4 the lifetime is reduced by approximate to 10% and decreases further with increasing He pressure. We assign this effect to the formation of Cs*He-n exciplexes, and determine the pressure dependence of the probability that the 6P(1/2) state decays via this nonradiative channel.