You could probably simply have diferent texts inside a div, then animate it to flip 180 and then fade out, as it fades out you animate the next one to fade in.
You create an interaction that flips it 180, but displays none half way through (when it is at 90 degrees and invisible since it doesnt have a thickness), and then display the next one in the same instant. I dont know how much you know about the software or webdevelopemt in general, so if you need a more indepth guide please tell.
If you look in their code it's not changing the text, it's displaying a secund text object.
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There are probably some javascrips out there that does this for you.