The hearing was also played a secretly recorded conversation between two Canberra Construction, Forestry, Mining and Energy Union organisers, Johnny Lomax and Zac Smith, discussing "the big fella" Kivalu "leaning on" building contractor Jian Yu He.

ACT CFMEU officials have previously said they did not know Mr Kivalu may have been corrupt until he admitted, at hearings in July, to receiving payments of more than $100,000.

On Tuesday the commission was told rumours had been circulating an unnamed organiser was on the take up to a year ago.

Mr Kivalu resigned as an ACT CFMEU organiser late in 2014 and also received a redundancy payment. He has pleaded not guilty to a charge of blackmail.

Jeremy Stoljar, counsel assisting the royal commission, put it to Mr Smith rumours had been "swirling around' about Kivalu receiving money by the first half of 2015.

Mr Smith said: "I don't recall hearing the rumours if there were."

Mr Stoljar then played the recording made at 5.12pm on May 22.

Mr Lomax, who was also arrested in July and has pleaded not guilty to blackmail, said a third party, Brad Jones, had spoken to him about a conversation with Mr He.

Mr Lomax said Mr Jones said when he spoke to Mr He about the union Mr He said: "Well, how much do they want this time?"

Mr Lomax said: "So obviously he's been touched before. By the sounds of this he's been touched by the big fellow."

Mr He told the commission on July 14 he paid Mr Kivalu $5000 in two instalments in or before 2013.

Mr He said: "He [Kivalu] said that without paying it's possible that I cannot stay in Canberra for work".

Mr Smith asked Mr Lomax: "Who's he [Mr He] dealt with before?"

Mr Lomax said: "I can only think of one other person."

Mr Stoljar put it to Mr Smith the person, while not named on the tape, was Mr Kivalu.

Mr Smith said: "Correct."

Kenneth Miller, another ACT CFMEU organiser, said he had heard Mr Kivalu may have not treated people fairly soon after he joined the union in 2012 or 2013 but no evidence had ever been produced.

"To my knowledge, up until the royal commission, [there were] no official complaints, no documents, no notes, [and] no phone calls [about Mr Kivalu]," he said.

"The union position has always been very clear. Any corruption would be dealt with strongly by the police."

Mr Miller was questioned about another phone tap, this one made on May 19, 2015, of a call between himself and assistant secretary Jason O'Mara.

They discussed a meeting Mr Miller had just had with Dave Taylor of Concept Cranes.

Mr O'Mara told Mr Miller: "I'll talk to you before organisers [a weekly meeting] and we'll work out a plan going forward because they are going to have an [enterprise] agreement."

Mr Miller replied: "Of course."

Counsel assisting the commission, Richard Scruby, put it to Mr Miller that Mr O'Mara meant if Mr Taylor's company wanted to work in Canberra it would need to have a union enterprise agreement.

Mr Miller rejected this: "Every company should have an agreement and pay the going wages and conditions and insurances to workers," he said.

"Whether we achieve that or not is another thing. It [what Mr O'Mara said could also mean] my job was to do my best to achieve that enterprise agreement. We have not achieved an agreement with Concept Cranes. It hasn't happened."

Mr Scruby put it Mr Miller he did not like saying "too much" on the phone because somebody might be listening.

Mr Miller said: "Well it's obvious you were."

In other developments ACT CFMEU organiser Anthony Vitler and legal officer Garry Hamilton denied any knowledge of price fixing by ACT construction companies.

Mr Vitler and Mr Hamilton were questioned over alleged price fixing by scaffolding and concreting contractors respectively.

The hearing continues on Thursday.