So you're a Calvinist too?
Acts 16:
30) And brought them out, and said, Sirs, what must I do to be saved?
31) And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
I'm not a Calvinist and i don't know what Calvinism is.
The statement you have quoted is true; one "believes" to be saved and belief is something in one's heart. No man can claim that this person and that person are saved and the other person is not. The kingdom of god doesn't come with observable signs that people will say there it and here it goes.
Even with what we believe our-self (within us), we can not claim that we are saved. Just as the name suggests, it is something at the end of a process and that process is salvation and salvation is God's work (not ours). We are required to maintain perseverance until the end so as to enter God's sabbath(rest) which means completion of His work.