This paper investigates the security performance of a joint unicast-multicast streaming system, where different users present heterogeneous mobilities. The orthogonal time frequency space (OTFS) scheme is employed to overcome severe Doppler effect caused by high mobility. The closed-form expression is derived for the maximum secrecy rate of unicast transmission with high privacy. Furthermore, the positive secure capacity probability (PSCP) of unicast transmission is also obtained and analyzed. Our analytical results show that compared with high-mobility eavesdroppers, low-mobility eavesdroppers pose a greater threat to unicast secrecy. Moreover, when the outage probability of unicast is greater than 1/2, more time frequency (TF) resources should be allocated to unicast, in order to guarantee the security performance of unicast.