None of this makes any sense.
"Both went directly into a Roth IRA."
That assertion does not seem to be supported by the Form 5498 that you have mentioned.
"I was told there is a 60-day window to change your mind and put the funds back into a Traditional IRA."
That would be true only if you had not "rolled over" to a Roth IRA (i.e. converted to Roth) the distribution from the traditional IRA.
It would probably help if you were more specific about the number of the box on the Form 5498 from the Roth IRA shows half of the total amount that was distributed from the traditional IRA.
A rollover from a traditional IRA to a Roth IRA constitutes a Roth conversion and Roth conversions are not permitted to be undone. It almost seems like the Roth IRA custodian treated one of the deposits as a trustee-to-trustee transfer from another Roth IRA, which conflicts with what you have described as the transactions that actually occurred. Another possibility is that you took a taxable distribution from the traditional IRA and used that money to fund a new Roth IRA contribution, but that's not a rollover. Knowing exactly what box on the Form 5498 shows half of the amount distributed from the traditional IRA would help to identify what actually happened.
I think that you are saying that the traditional IRA was established by a rollover from the federal TSP, but that's not germane to the subsequent distributions from the traditional IRA.
