Apart from that, the sheer amount of Turkish immigrants who left the country in the last decade (including me) are not Erdoğan supporters. However, many of us refrain from heavy criticism as we occasionally go to Turkey to visit our relatives and we don't want some specific person having a bad day destroying our lives.
So you usually hear the other side and may mistakenly think that "expat Turks" support Erdoğan big time. The majority of votes he gets from Turkish immigrants are the Turks who left the country more than a couple of decades ago and partly, their children. The "why" has a complicated answer that touches religion, demographic dynamics and acceptance in society.