Alinka – yours is a perfect example of the tail wagging the dog!
The Strata Manager works for the Owners Corporation (i.e. you and the other Owners) and they’re obligated to act in accordance with your instructions provided they’re legal in terms of the NSW Strata Schemes Management Act (SCMA) and any other Acts of relevance.
Even though the Agency Agreement that prescribes the terms of your Strata Manager’s appointment and their duties may delegate the role of Executive Committee Secretary to them, which gives that Strata Manager the ability to convene General Meetings, even then the elected Secretary of the Committee can, and in your circumstances should have, overruled the Strata Manager.
The correct procedure was followed when 25% of Owners (by unit entitlement) requisitioned the delegated Secretary to convene an Extraordinary General Meeting (EGM) but the SCMA then requires the Secretary to convene a Meeting to consider the Owners’ Motion/s “as soon as practicable” thereafter.
Clearly, in the circumstances you describe that should have been concurrently with the upcoming Annual General Meeting, and any Strata Manager worth what their client’s paying them (i.e. your Owners Corporation again) should have been in no doubt about the requirement for special resolutions, with ≥75% of votes in favour by unit entitlement for the Motion/s to pass; the SCMA is very clear on that provision!
It’s usual for an EGM to be paid for by the Owners who’ve requisitioned it, but because the Motions were incorrectly put and the 2 hour debate resolved nothing in terms of committing expenditure, resulting in a proper mess (a technical term) I’d be inclined to let it slide and pay-up from communal funds. After all, those 2 Owners are contributing at least 25% of those costs anyway!
So far as the Strata Manager is concerned, your Executive Committee needs to quickly pull them into line. Let them know who they’re working for, and if necessary amend their Agency Agreement to ensure that happens – perhaps by reviewing those delegations.