Nothing at all - it’s able to picked up as meaning different things though
What Evangelical Protestants mean by it is the Saviour Who “loved me and gave himself for me”: the Evangelical is making those words of St.Paul’s in Galatians his own as well - the Evangelical’s emphasis is on the fact that Christ has saved not only others, but him also. IOW, he is among those who are loved by the Saviour, Who is his no less truly than theirs. And love is an act of one person to another - nothing could be more fully personal than God’s Love for each one of us; not least because that Love is a Person, Who died as fully for each person as though there were no others.
As for individualism - Calvinists are Evangelicals, and though they seem not to use the exact words (so far as ICR), they do insist strongly on personal religion: as reading the Puritans & their successors makes abundantly clear. And Calvinists have a high doctrine of the Church; as did the Puritans. They have Baptism in the Name of the Blessed Trinity just as we do; they even use the word “sacrament” for it on occasion.
Some Catholics seem to understand it as a claim that the Evangelical is saying “He is my Saviour - & no one else’s”. Which is something entirely different.
IMO, Catholics can seem to be so keen to reject that claim (in either meaning or both ?) that they sometimes risk de-personalising life in Christ; as though the ideal attitude between Christ & Christians were closer to impersonality, & to the loss of the individual in an anonymous crowd. Which is pretty much what society tends to be like. Father Faber at least would not have understood that at all.
Sometimes it looks as though Protestants will be criticised ***whatever ***they say
As for the title, it over-simplifies: because Christ is the Mediator, & the Spirit is His also - Christ-centredness, is not Christomonism. To be Christ-centred looks after itself, because it is not directed to itself, but to Christ; Who is not confimed to our ideas, but is their Lord; as He is of all things. He can’t be told what to do - thank goodness