They told staff to find the money in existing budgets, refusing to approve any additional capital funding.
Construction of the new urban space started mid-year and all but the toilet block refurbishment - put off until after summer - was on schedule to finish by December.
Councillor Leanne Brown said the community was expecting a high-quality result.
"It will be what we said it was going to be - a first-class facility for the community to enjoy."
A concept design of the planned urban open space on Maunganui Rd. Graphic/Tauranga City Council
Mark Rundall, owner of Artastic Print Place on Maunganui Rd and a longtime critic of the green space plan, said the overspend was "ridiculous".
"If the council has to find another half a million they may as well get the bulldozer out and flatten it down and turn it back into a car park."
He said he heard regular complaints from customers about the lack of parking since construction began and his revenue was down 10 per cent on this time last year.
Jaine Lovell-Gadd, the council's general manager of city transformation, took the blame for the budget oversights that led to the overspend.
She said the budget done in 2015 should have been reassessed before the funding decision came up again, post-consultation, in April 2017 - but was not.
A new budget estimate in August 2017 put construction costs well over budget, partially blamed on a citywide escalation of construction costs.
It prompted a redesign of the concept plan and renegotiations with contractors, only recently completed.
A detailed design of the plan for the new urban open space being built on the site of the former Phoenix car park in Mount Maunganui. Graphic/Tauranga City Council
Lovell-Gadd said the redesign aimed to reduce costs without reducing the quality or features the council told the community it would deliver.
Mount Mainstreet manager Ingrid Fleming said the organisation's board had received assurances from the council that the major elements would not be significantly affected.
"We are very happy that the council understands the importance of a good quality space in the heart and soul of Mount Maunganui, for both tourists and locals."
It was also important the space opened on time as it already had bookings in January including the We Run The Night running festival and the return of Sunday farmers' markets.
