The Kaiārahi experienced steering problems during its 3.30pm voyage across the Cook Strait to Picton.
The vessel returned to Wellington as a precaution and docked at 10.05pm.
A North Island man on board said passengers were not able to collect their bags until more than 30 minutes later.
The union's national secretary, Carl Findlay, said what happened proves why the government should not cut the contract on an emergency tug, as announced last month.
The government said it had decided to end the contract for the MMA Vision in February - months ahead of time - saying the costs outweigh the benefits.
"We need the [MMA] Vision available because it's the only rescue operation that we have available," Findlay said.
"Chris Bishop has recently come out and said he's going to cut funding, which is absolutely crazy."
Findlay said the funding for the vessel was very small.
He was open to meeting with the Bishop, the Transport Minister, to discuss saving the tug.
"We should write to him directly. But in saying that too, he seems like a reasonable sort of a guy - he should come and talk to the experts in the industry, and we represent that workforce. We're quite happy to talk to him."
In the meantime, Findlay said he wanted answers.
"It's ongoing, what's happening with the Interislander ferries and it's well documented. So again, I don't understand why he wants to cut the funding on this very important piece of New Zealand marine security.
Wellington harbourmaster Grant Nalder earlier told RNZ crew still had "full control of the wheel", despite what he said was a "technical problem with the steering".
"As they were approaching Tory Channel and did their regular checks, they found something was behaving oddly with the steering.
"They didn't go through Tory Channel, just went out into Cook Strait to test what it was. After doing that, they decided they were going to return to Wellington."
Interislander executive general manager Duncan Roy said technical staff would be investigating the problem.
"The issue became apparent as part of standard procedures prior to entering Tory Channel and the return to Wellington was decided on as a safety precaution rather than sailing through the Sounds."
"The appropriate authorities have been notified, and we will work with our passengers and freight customers to reschedule them."
