Did the evil present within anyone "choose Jesus to save them?" It never happened.
The bible throughout says that by our deeds we will be judged. The cross is a part of that. God opens our eyes, and ears, to His truth. If our heart softens toward God, we will accept it, if we have heardened our heart in sin, we will reject it. MAny people stuggle for years "deciding" if they willl follow Christ. There are many arguments for and against, we gravitate toward a decision.
Joh 3:18-21 "He who believes in Him is not condemned; but he who does not believe is condemned already, because he has not believed in the name of the only begotten Son of God. And this is the condemnation, that the light has come into the world, and men loved darkness rather than light,
because their deeds were evil. For everyone practicing evil hates the light and does not come to the light, lest his deeds should be exposed. But he who does the truth comes to the light,
that his deeds may be clearly seen, that they have been done in God."
Salvation definitely has a "deeds" component.
Joh 14:22-24 Judas (not Iscariot) said to Him, "Lord, how is it that You will manifest Yourself to us, and not to the world?" Jesus answered and said to him, "If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him and make Our home with him. He who does not love Me does not keep My words; and the word which you hear is not Mine but the Father's who sent Me.
There is definitely a point where God opens our eyes, but our reasoning, choices, deeds, are important to the outcome.
Job 36:10-12 He also opens their ear to instruction, And commands that they turn from iniquity. If they obey and serve Him, They shall spend their days in prosperity, And their years in pleasures. But if they do not obey, They shall perish by the sword, And they shall die without knowledge.
Each of us daily make choices to sin or not, temptation is daily before us. But we must all strive against it.
Heb 12:4 You have not yet resisted to bloodshed, striving against sin.