After trying a few times, and succeding once, I am leaning towards the "success is rolled when persuasion starts" or "non-cumulative chance" theories.

Example of rolled
out of 2000, the system randomly picks 846 wil be when you get hero.

Example of non-cumulative
If the hero has 2000 max, then each point is .05 % chance. So giving 1 rose has .05% chance to get hero, but 20 rose at once will give 1% chance. Or giving 5 perals at once will be 2.5% chance. These chances will stay the same, even if you have the hero at 900 persuasion right now.