Nash described the controller as a "clown".
Airways apologised to Nash, also on Twitter and said the delay was due to an "unexpected staff shortage".
"Unfortunately this came after a controller had a car breakdown en route to work last week. While unrelated, we regret these two issues have inconvenienced passengers," a spokesperson posted on the social media site.
Eastern Police confirmed officers were deployed to the Napier air traffic control tower at 4pm on August 5.
Officers were called to a reported "disturbance" but police could not give any further details.
No arrests were made or charges laid as a result of the incident.
Airways - the company that provides air traffic control and infrastructure across New Zealand's airports - also confirmed the incident.
"We are aware of the events that occurred at Napier Tower on August 5," spokeswoman Emily Davies said.
"Police presence was requested to assist in evicting a previously authorised visitor in order to maintain operational safety requirements.
"The matter was resolved before police arrived and no action from officers was needed."
Davies said Airways had undertaken a review of the situation.
She confirmed no policies or civil aviation rules were breached.
"Furthermore, there was no disruption or impact on the service provided to any flights," she said.
"Safety is our highest priority and we are confident that the robust procedures we have in place for facilitating visits to the tower ensure that the safety and security of our staff and service is maintained at all times."
Davies said the team at Napier tower safely managed about 24,000 flight movements annually.
"Air traffic control is a highly skilled role and our controllers undertake regular and ongoing professional development and training," she said.
"We are confident that all our operational staff at Napier tower are fit for duty."
Hawke's Bay Airport operations manager Gareth Mentzer said he didn't see any reason why passengers should be concerned.
"We have a strong working relationship with Airways staff both locally and corporately and continually work together to identify ways to enhance safety and serviceability."