In general, there are no federal tax consequences on the creation of a trust. However, the fiduciary of trusts must file form 1041 with the IRS which details the income, losses, and gains of a trust. Form 1041 is here:
and the instructions are here:
In general, trusts are considered "pass through" entities because any income that is paid to a beneficiary is a deduction to the trust. The beneficiary then reports this income on their personal income tax return as income. The trust must also issue a K-1 to the individual in addition to filing form 1041.
If the funds of the trust do not get distributed to the beneficiary until the death of the settlor, as is the case with a Totten Trust, then the beneficiary will not have income until the proceeds are distributed. The settlor also will not have gift tax consequences when the trust is created.
Trusts are set up to avoid probate, which means when the settlor of the trust dies, the trust continues in existence without the need of going through probate -- or in this case, the proceeds are distributed to the beneficiary on the death of the settlor.
The terms of the Trust will dictate when the funds pass to the beneficiary. If the intention is to have the funds pass to the beneficiary on the death of the second account holder, this can be accomplished in the language of the trust. Watch out for gift tax and income tax consequences, though, on the passing of funds from the first joint bank account holder to the second joint bank account holder if the second joint bank account holder did not contribute any of the funds, and received 100% of the funds on the death of the first joint bank account holder.