Gillespie first presented to the council in February.
Contact and the council gathered for a tour of the proposed site before the council meeting in Roxburgh on Thursday.
Representatives of Ngāi Tahu were also present.
This week's council meeting agenda stated Gillespie was to present the hatchery design to the council at its pre-meeting field trip.
The proposed hatchery site inspection and update was not open to the public or media.
"It is part of a negotiation between the two parties [Contact and the council] and there are some sensitivities around that," council chief executive Ian Hadland said.
However, Hadland told the Otago Daily Times following the meeting the tour had been "very positive".
The meeting agenda stated Contact staff had proposed a review of the Lower Clutha Sports Fish Management Plan - negotiated as part of the consent conditions for the dam operation - and its "ongoing relevance and application" as it was now a decade old.