Should a 1099-Q trigger tax when it is a trustee to trustee transfer?

No, it shouldn't.  You may have answered something wrong in the interview.   Did you indicate that Box 4 (Trustee to Trustee transfer) was checked?

Per the instructions to the recipient (page 3), Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return.  When none of the distribution is taxable, TurboTax will enter nothing about the 1099-Q on your tax return.   TurboTax will prepare a 1099-Q worksheet for your records, but the worksheet is not sent to the IRS.   In this case, just keep the 1099-Q with your tax records, but don't enter it.  

Earnings that were part of trustee-to-trustee transfers are generally not taxable.   Reported earnings are taxable if they are part of a nonqualified distribution— a withdrawal that was used for any other purpose besides qualified education expenses.  Here's more info on Form 1099-Q. 

See Slide 6