I'm skeptical about what TDA told you. The IRS has announced (https://www.irs.gov/newsroom/taxpayers-should-file-by-july-15-tax-deadline-automatic-extension-to-oc...) that is not extending the date from July 15 to August 15, at least in regard to the filing deadline for 2019 tax returns, and I suspect that that applies to all other items that had the deadline extended to July 15 as well. There is presently no mention on the IRS website of such a change and presently no IRS Notice published on the IRS website superseding IRS Notice 2020-23, nor can I find any mention of such a change anywhere on the internet, including sources that I follow that report things like this almost immediately.
It seems more likely that the person who told you this is confused between the extended deadline under the disaster declaration and the August 31, 2020 deadline for those who received a distribution that would have been an RMD were it not for section 2203 of the CARES Act to repay the distribution to the distributing IRA, described in IRS Notice 2020-51 issued on June 23, 2020.
Given that the July 15, 2020 deadline has not yet passed, it makes sense to do the rollover by July 15 rather than risk having received bad information from TDA. However, that still leaves a bit of time to get the information from a more authoritative source (the IRS) if they really did make the change. The IRS generally makes such announcements the same day the changes occur: https://www.irs.gov/newsroom
