It certainly applies to Christians. Having God's Spirit doesn't mean a person becomes immune to Satan's influence. The difference between a truly converted Christian and everybody else is that they are aware of Satan's influence and don't mindlessly operate under it like everyone else does(Eph. 2:1-3). Rev. 2 and 3 shows all but 2 church eras surrendering to Satan's influence because they drifted back into relying on their own reasoning. When Paul spoke of the sins he committed as a Christian, he described himself as a carnal being who was still prone to sinning(Rom. 7:14-24). This should highlight how hard Satan fights to bring converted Christians back under his influence.
When the Bible speaks of God saying He will give someone a new heart, it's a poetic way of saying the person will have a newfound desire to live by God's laws and commandments. For example, look at the prayer David wrote in Psa. 51 where he asked God to give him a new heart. David recognized how much he had began worshiping his own reasoning when he committed adultery with Bathsheba, tried to pass the unborn child off as Uriah's by getting him drunk and telling him to have sex with Bathsheba, and then arranged for Uriah to be killed in battle by enemy forces when that didn't work.
Despite what a lot of adherents of mainstream Christianity may believe, biblical Christianity is just as much about resisting Satan's influence as it is about cultivating a relationship with God. It is for this reason that Christ told multiple church eras to overcome Satan like He did. The temptation to rely on their reasoning is going to be there for Christians in this age.