I am unclear as to your concern here, bashmark.
Are you concerned that the city council could be violating the Open Meetings Act by negotiating the terms of a contract without public input, or are you curious about the way the council chose the multi-national company's proposal over the other four submitted? Or is it something else entirely?
Your city council is governed by state law, city ordinances, and the city's policy and procedure guidelines. You may wish to check out the articles of your city's charter for the provisions that apply to RFPs and the negotiating and awarding of contracts.
And you could check out the Washington's Open Meetings Act (RCW 42.30), which governs what the city can and can't do "behind closed doors." The city council is allowed to hold executive (non-public) sessions, to discuss select matters as permitted under RCW 42.30.
But I, like Cdw, do not see anything off-hand that seems wrong or unethical with the council's conduct, based on the limited facts presented here so far.