"What's interesting is he's writing them at two and three in the morning and that sort of thing and I've told him to try and settle down," Jones told Radio Sport's D'Arcy Waldegrave.
"He made a bit of a fool of himself."
According to Jones, Higgins was so upset by O'Connor's appointment that he feared the fight wouldn't go ahead.
"Two days ago I didn't think it was going to happen because David was getting so carried away.
"As I said to David in a letter yesterday, he's got to bite the bullet on this one. It's too late now. He's carrying on about the referee . . . He's not trying to engender publicity, incidentally. He genuinely is concerned about this.
"I said, Joseph's either up for this or he's not. Simple as that. You've got to sit back and forget it."
Jones believes the Parker camp is worried about losing to Fury, who backed out of the original bout at the 11th hour in April, leaving Parker to defend his title against little-known Romanian Razvan Cojanu.
"Fury's not a very good opponent for Joseph. He's long and rangy and Joseph hasn't done particularly well against those sort of chaps. He could well lose," Jones said.
"I was in Britain when [Anthony] Joshua beat [Wladimir] Klitschko [for the IBF, WBA and IBO heavyweight titles in April] and the whole nation stopped. It's become a bit of a religion. People obsess about Joshua.
"You can't turn up there [in England] and say you're the world heavyweight champion and you're fighting the number five in Britain, that hasn't fought in 18 months and expect much public interest. Consequently, there isn't any.
"They can't sell tickets, no TV channel will take the pay-per-view. They're going to lose millions and another factor that's hurtful for him [Higgins] - I suspect they won't sell that well here [in New Zealand] because we have an election on Saturday and that's dominating the news.
"And also there's a little bit of suspicion now about Joseph after recent performances that perhaps he's not quite up to what they thought he was."
Jones, however, doesn't see Higgins' actions affecting his future relationship with Parker.
"It won't be the end of the line because David's very passionate about Joseph. He really is. He should stand back a bit and be a bit more level-headed," Jones said.
"David's out of his depth there, frankly. He genuinely believes there's a conspiracy going on, thus the performance this morning and it was very embarrassing really."
