Jim McColl is backing a group of shareholders who hope to have former chairman Malcolm Murray, Paul Murray, Scott Murdoch and Alex Wilson appointed as directors at their delayed Annual General Meeting next month.
Somers, a chartered accountant and investment manager, joined the board on Thursday just as the AGM was confirmed for December 19, a move that comes with turmoil continuing to plague the League One club off the pitch.
But McColl's group has questioned the appointment and repeated their desire to find out if former chief executive Charles Green is still involved with the club through shareholders Blue Pitch Holdings and Margarita holdings.
They also want answers about the continuing 'poor financial performance' of the Ibrox club, who reported a £14m operating loss for the 13 months to June.
Their statement read: "We note the appointment of David Somers as acting chairman of Rangers International Football Club with bemusement.
"Is he purely independent and there to ensure the AGM is conducted properly or is he endorsing the current dysfunctional regime and trying to rebuild it?
"The Court of Session ruling was nearly four weeks ago and the spirit of it would have had the AGM done by now and democracy would have been achieved.
"His gushing praise of the history of the club has been done by many characters in this revolving door regime.
"The fans are well aware of their history and instead need to hear answers to the questions they ask vocally at every game about investors' identity, Green's involvement and poor financial performance.
"Last year's prospectus promised a high level of corporate governance. The result has been a disgrace. Mr Somers says he stands for corporate governance. As none of us know Mr Somers we have asked Daniel Stewart (Rangers' advisors) for an introductory meeting.
"Our group is ready and fully equipped to rebuild the club financially and morally and although we are being pressed by shareholders to call for a general meeting we will wait in the interests of the dwindling cash balance.
"We and they, however, will not stand for further appointments pre AGM."