I believe you are correct that the Export function is not working properly (it happens with me too) - ie, it is not attaching the embedded camera profile to the exported file. You must file a support case with PhaseOne here;http://www.phaseone.com/My-Account/Login.aspx?transferPath=http://www.phaseone.com/en/SupportMain/ContactSupport.aspx
and supply screenshots and explain yourself as you've done here. Sorry, you will have to repeat yourself.
But the 'correct' way to convert (export) files to tiffs using CaptureOne is via the Process recipes in the 'Output' tool section. This is how most people do it. I never use the Export function.
If you're new to CaptureOne you should have a look at their free training online; http://www.phaseone.com/webinarshttp://www.youtube.com/playlist?list=PLDMRz3ssFQH6HhCcWLh7xL0SapRxUNzs9