We present findings from a qualitative study with 28 participants of the dyadic intercultural communication tensions professionals experience in Face-to-Face (FTF) and Computer-Mediated Communication (CMC) workplace interactions. We identify four categories of intercultural communication tensions that emerged most frequently in our dataset including range of emotional expression, level of formality, "fixed" versus flexible appointments and task versus social-orientation. We discuss how these tensions manifested in FTF and CMC media and unravel the ways media supports or hinders intercultural communication. We present the adaptations participants made to mitigate such tensions and offer implications for design. Our findings demonstrate that the most frequently occurring intercultural communication tensions manifested in both FTF and CMC, regardless of the medium used. This indicates that cultural communication challenges will persist no matter the medium, highlighting the opportunity for technologies to better support workplace intercultural communication.