Salomon started his banking career in 1997 at GE Capital Multiservis, where he held the roles of chairman of the board of directors and CEO.[3] By 2000, he took on the position of Director of Retail Banking and became a member of the board of directors at GE Capital Bank, overseeing sales and marketing.[4] From 2004 to 2007, he then assumed the role of chairman of the board of directors at Poštová banka in Slovakia.[5][6] Between 2008 and 2012, Salomons focus shifted towards private investment projects, and he instigated a project to establish a mobile payments platform in the Czech Republic called Mobito. The platform was operated by Mopet CZ, where he served as CEO.[7] Mobito was not a success however,[8] so in 2013 he joined Slovenská sporitelña as a board member, becoming Director for Retail later on.[6] Since January 2015, Salomon has been a board member at Ceská spořitelna, subsequently replacing Pavel Kysilka as CEO in January 2016.[4][9]
On 16 June 2023, after being president for three years, Salomon became first vice-president of the Czech Banking Association. He was succeeded by the previous first vice-president, Jan Juchelka.[10] He also is a member of the Scientific Board at the Prague University of Economics and Business.[11]