You're pedantically correct, but in a way that's irrelevant unless the Electoral College sees its electors vote against the wishes expressed by the public in the public elections (which is now legally restricted from happening in the majority of states anyway).

Realistically, unless there's either effectively a coup by the Electoral College, or an incredibly close election that needs to wait for recounts or a runoff (second) public election in one or more states to know who the president will be, the president is known after the public election even if the paperwork for the votes that technically elect them don't happen until a couple of months later. So I'd consider the comment you replied to to be more true than yours despite yours being technically more accurate.