The Senate started doing the audits after a June 2012 auditor general's report was critical of the way some senators reported their expense claims.
"That's why Senator Wallin was referred," Tkachuk, who is chairman of the internal economy board, told reporters, "and [she] was referred well before this issue came up …. She was No. 1."
He was referring to the issue of residency and travel expense claims that have dogged Conservative senators Mike Duffy and Patrick Brazeau and Liberal Mac Harb, the three whose expense claims were referred to external auditor Deloitte Canada.
Wallin has confirmed that she met with Deloitte to answer questions and provide documentation about her travel claims.
Tkachuk said that the results of the random audits will not be made public. But Government House Leader Peter Van Loan said late Thursday that it was his expectation, and, he added, the government's expectation, that the reports would be made public.
Van Loan told host Evan Solomon on CBC New Network's Power & Politics that he meant all the reports on senate expense claims should be released publicly, including the results of the Deloitte audits, although he prefaced his answer by saying the decision was up to the Senate.
Wallin, who was nominated by Prime Minister Stephen Harper as a senator from Saskatchewan, has explained that she often flies to Toronto and stays overnight before taking an early-morning flight to Saskatoon. That avoids a late-night drive to the remote town of Wadena, where she says she lives.
File under review
Wallin said the fact that her second ticket doesn't originate in Ottawa means the flight isn't counted as one of the regular flights she's entitled to, since the receipt must show that the trip is from the National Capital Region to Saskatchewan.
Asked by CBC if the Senate would insist on a ticket being routed in this way, Senate communications replied in an email, saying, "This file is under review, so we can't comment on it."
Questions have arisen about Wallin's travel claims, because she still owns a residence in Toronto and was living in the city when she was appointed to the Senate.
Wallin is entitled to claim for trips to and from Saskatchewan, but not for trips to Toronto and back unless she has senate-related business in the city.
When CBC News tried to reach Wallin Thursday afternoon, her office said she was on her way to Saskatchewan.
Auditor General Michael Ferguson's report in June noted that "Senators operate on the honour principle, with their signatures attesting that the expenditures have been incurred in carrying out the performance of parliamentary functions."
However the auditor general complained about the lack of details in some senators' claims.
For instance, he said, one senator took a trip to Washington and provided no details beyond saying the visit was for "parliamentary business."
Senators can be compensated a daily rate if they own a secondary residence in Ottawa on the grounds that staying in a house or condo is cheaper than paying hotel bills. The rate is about $28 a day for 365 days for a residence the senator owns in Ottawa.
But the auditor general found that of the seven cases tested, two senators did not provide proof that they owned the secondary residence for the whole year.
In May, just before the auditor general's report was released, the Senate tightened up its travel rules, noting, "Spending public funds on travel is a sensitive matter and sound judgment must be exercised when travel-related decisions are made.