This is a strange one but first and foremost, there is no legal process for the co-option of councillors. Once the deadline on the notice inviting a by-election has lapsed, it is down to the council to co-opt and how they wish to do that is down to them.
You mention that they had a prejudicial interest - I can only assume that they did not have a pecuniary interest? If it was non-pecuniary, there is no requirement to remove themselves from the meeting. They have every right to vote on the election of councillors.
Whether the council choses to undertake co-option in a closed or open session is up to them. It is perfectly legal to ask your mate down the pub to join the council and they would effectively be elected. For what it is worth, our co-option meeting are held privately as we have more candidates that places and therefore, if they are being asked personal questions (ie "Tell us a bit about yourself and your background") about their application, it is not for public dissemination until they are elected.