Absolutely false.

You merely have to know that your opinion contradicts Church teaching and adhere to it anyway.

Pertinacity is the opposite of things like where you mis-speak, a slip of the tongue, or just say something in passing and then as soon as you're corrected on the matterm you retract it.

In all things, the litmus test is if you knew that your opinion was condemned by Church teaching, you'd abandon it, vs. ... you just don't care and you decide that the Church is wrong.

If some erstwhile Catholic were to say, "I know the Church teaches that Our Lord is present in the Blessed Sacrament, but I don't believe it.  I think it's just a symbol."

That doesn't require admonition.  That person is a manifest heretic.  Most of the time, such as these simply leave the Church ... and there's no formal warning, correction, or admonition required for everyone to realize that this guy does not have the faith and is not Catholic.  So every one of the millions who abandoned the Church after Vatican II, they all were considered Catholics until they got their 2 admonitions?  Church doesn't have time, nor does it need to waste time declaring the obvious.

If some erstwhile Catholic announces, "Yeah, Catholics are wrong, and the Orthodox are right." and then starts going to an Orthodox church ... that person ceases to be Catholic, and no warnings or corrections are required.  We've had a couple posters here decide to become apostate by declaring their allegiance to the Orthodox.

Does it require admonition / correction (even one, much less two) in order for it to be objectively true that those people are no longer Catholic?  Or course not.

That's Prot-like interpretation of Scripture regarding the 2 warninings.  It's not necessarily in all cases.

So, it's a theological term, the distinction between some of the "5 Opinions" regarding a heretic pope.  It's opposed to an "occult" heretic.  There's one opinion (held by very few) that occult heresy removes someone from membership in the Church, so "manifest" is used simply to explain that you don't hold that heretics simpliciter lose membership in the Church, by excluding occult heresy.