The recipe seems to foresee what you had happen:
QuoteThe butter will seem to pool out of the mixture, and you may notice a few specks of curdled egg, but that’s a-okay.
And the author states at the beginning:
QuoteI don’t know how anything so curdled, coagulated, lumpy, and broken can turn out so
delicious, but this pie manages to defy the odds.
You are dealing with adding eggs to a warm caramel, so I don't think you can expect it to behave as a plain caramel would, and I would anticipate all sorts of ugliness occurring. But how did your pie turn out?