God's presence in our hearts is not an alien presence inside of us. When we love someone, we love that person in spirit (in our "hearts") and that person's "presence " is said to be spiritual and not physical.
We are not invaded. When we fall in love with God, He is on our minds and in our consciousness; we are aware of His existence. When we do things with God in our hearts, we act according to what Christ taught us, we remind ourselves of what He said not to do. We do it out of love.
He is our motivator and mover, and when we sin His awareness in our minds helps us come to grips with our error, so we can repent for our ingratitude and ask for forgiveness.
But that doesn't match the language the Bible uses. When you love someone, do you say you have been given something? No, if anything you are the giver (of your love). So, the Bible can't mean that you just start loving the Spirit. It's much more than that. Jesus said He will SEND. That is something from Him TO us. The language used is not metaphorical.