RMDs, Rollovers and First-Dollar-Out rule -- Confused

TLDR; I did a trustee to trustee direct rollover from IRA 1 -> IRA 2 before I took my RMD out of IRA 1. Custodian/trustee 1 sent a check directly to custodian/trustee 2. I did later withdrawal/distribute all IRA RMDs properly and in the time required. Is this a problem for the IRS? Details: * I did not do a rollover from a company plan (aka a 401k) to an IRA. It was IRA->IRA. * I did not have a check made out to me from IRA 1 and sent to me which I later put into IRA2 (aka a 60-day indirect rollover). The funds did not go thru me. * It was a partial rollover. I did not rollover the full amount that was in IRA 1. I keep seeing different answers to this, and am concerned that, because of the First-Dollar-Out rule, the IRA1 RMD amount within the IRA1-IRA2 rollover is considered a distribution and is taxable. I think maybe part of the issue is I don't understand the difference between a trustee to trustee rollover and a direct rollover. Are they the same? I was under the impression that, as long as I pay the RMDs properly and on time, all is good?? Any help greatly appreciated.