In this work, we analyze the secrecy outage performance of a dual-hop relay system composed of multiple-input-multiple-output radio-frequency (RF) links and a free-space optical (FSO) link while a multiple-antenna eavesdropper wiretaps the confidential information by decoding the received signals from the source node. The channel state information (CSI) of the RF and FSO links is considered to be outdated and imprecise, respectively. We propose four transmit antenna selection (TAS) schemes to enhance the secrecy performance of the considered systems. The secrecy outage performance with different TAS schemes is analyzed and the effects of misalignment and detection technology on the secrecy outage performance of mixed systems are studied. We derive the closed-form expressions for probability density function (PDF) and cumulative distribution function (CDF) over Málaga channel with imperfect CSI. Then the closed-form expressions for the CDF and PDF of the equivalent signal-to-noise ratio (SNR) at the legitimate receiver over Nakagami-m and Málaga channels are derived. Furthermore, the bound of the effective secrecy throughput (EST) with different TAS schemes are derived. Besides, the asymptotic results for EST are investigated by exploiting the unfolding of Meijer's G-function when the electrical SNR of FSO link approaches infinity. Finally, Monte-Carlo simulation results are presented to testify the correctness of the proposed analysis. The results illustrate that outdated CSI shows a strong effect on the secrecy performance of the mixed RF-FSO systems. In addition, increasing the number of antennas at the source cannot significantly enhance the secrecy performance of the considered systems.