The secret is that David, Rosalind, and the others can all communicate through telepathy. They do not have to see each other. They do not have to touch each other. They can simply communicate with each other in each other's minds.
The Strorm household is basically devoid of any kind of decorations. Joseph Strorm is a religious "man of consequence," and his house reflects it. The only "decorations" that are up around the house are some wooden panels with sayings from the "Repentances" burned into them. They say things like:
ONLY THE IMAGE OF GOD IS MAN
KEEP PURE THE STOCK OF THE LORD
BLESSED IS THE NORM
IN PURITY OUR SALVATION
WATCH THOU FOR THE MUTANT!
Basically the sayings all urge uniformity. The people in the book are only accepting of the image of man that they know. Any deviation from that is not normal, and therefore not keeping the Lord's creation pure. Without pure uniformity, salvation is lost. That's why the people need to be on the lookout for any genetic mutations (deviants). David is a deviant. He has some kind of genetic mutation that allows him to telepathically communicate with other similar deviants. Uncle Axel knows the danger that David is in, which is why (in chapter 4) Uncle Axel tells David to keep it all a secret.