The Donegal-born stand-up comic was said to have singled out British Secretary of State Karen Bradley and a number of unionists, including DUP leader Arlene Foster, for particular attention.
But other people who were at one of his shows said Tiernan took a pop at both sides of the political divide, not just unionists.
A Belfast DUP councillor said he was contacted by constituents in the audience who complained that they had been deeply offended by Tiernan’s “anti-unionist” remarks.
In a tweet, Councillor Dale Pankhurst said that he’d had “numerous calls from unionists who had to get up and leave the Tommy Tiernan concert (actor in Derry Girls) in the Ulster Hall due to comments made regarding contentious issues”.
He said he understood that some people had asked for a PSNI investigation to be started.
One concert-goer who didn’t want to be named said Tiernan used four letter words to describe a number of politicians.
“He really overstepped the mark. I’m slow to anger but setting aside what he said and who he said it about, it was his language which I found to be completely misjudged,” they said.
Tiernan, who plays a downtrodden father in Derry Girls, is known for his outspoken attacks on a wide range of individuals and organisations, including the Catholic Church, during his comedy routines.
On social media, a number of people said they had been surprised that Tiernan had included so much material on politics and religion in Belfast.
On Facebook, one man said in a message to the comedian: “Went to see the show last night at the Ulster Hall.
“Really disappointed in the political stuff. I didn’t think you done all that.
“Only made bearable by the fact the sound system was awful and we could hardly hear. We left half way through.”
Another poster said he had loved the Ulster Hall show on Sunday night but added that “it had been marred by a five minute political rant about the DUP and about East Antrim MP Sammy Wilson”.
He added: “Surely Tommy your own personal political views shouldn’t be turned into a political rally on stage?”
Tiernan had three sell-out shows in Belfast over the weekend, one in the Waterfront Hall and two in the Ulster Hall.
One person at the Friday night show in the Waterfront said there wasn’t anything overly offensive and he didn’t notice anyone walking out.
One online poster compared going to a Tiernan gig with attending a concert by the Wolfe Tones and being offended at hearing a rebel song.
Another said that Mr Pankhurst had ensured that Tiernan’s next few gigs would be sell-outs.
Tommy Tiernan’s management in Galway said it wouldn’t be making any comment on the claims about the Belfast shows.
Two years ago the BBC apologised for an “inappropriate” joke that Tiernan made in a Radio Foyle interview about Mrs Foster
* The second episode of series two of Derry Girls goes out on Channel 4 tonight, Tuesday, March 12, at 9.15 pm. Last week’s first episode of the new series hit 1.8 million viewers.