Mr Arber, wearing only a pair of dark shorts, introduced himself as Paul and said he was in the city for a tennis tournament.
He could not be convinced to return to his accommodation and was last seen walking back towards the river.
Mark Sheppard, who runs Kanga Tennis Tours and was with Mr Arber earlier, said the news gave him hope.
"We had feared the worst that something could have happened, that he had been mugged and taken away and abducted," he said.
"That doesn't mean it still can't have happened, but at least we know it didn't happen in Hamilton East and there is something gone possibly a bit haywire with his mental state."
Mr Arber was in charge of eight youngsters who with a large group went to get something to eat after they finished their tournament about 8.30pm on Saturday.
He was supposed to return to the minivan at 9.30pm but didn't.
"What he did was he gave 20 bucks to a homeless person, then he walked over to an ATM, then he walked across the road, patted a dog and that was the last we saw of him, said Mr Sheppard.
"He disappeared up Grey St and we never saw him again."
He said Mr Arber had been "a bit vague" with his pupils before he disappeared.
Detective Inspector Karl Thornton said Mr Arber's behaviour was out of character, and friends had described him as being "somewhat distant and spiritual" before he disappeared.
His parents, Sam and Richelle Arber, who arrived in Hamilton on Monday, described him as a "gentle, spiritual person" who was harmless towards other people.
Mr Thornton said Mr Arber's wallet and the keys to the minivan had been recovered. It appeared nothing had been taken from his wallet.
Police yesterday increased their search efforts, with a boat on the Waikato River, the Eagle helicopter doing an aerial search and officers scouring the riverbanks.
They want to hear from anyone who might have seen Mr Arber and would also like to hear from the homeless man to whom he gave money and the couple whose dog he patted on Grey St.
