CDT agents don't consider the acausal impact of their decisions when choosing actions. Whenever a CDT agent is put in a situation where it has to make a decision, it considers multiple hypothetical worlds, one for each decision it could make. In a CDT agent, the only difference between these hypothetical worlds is the decision it makes. This means that when CDT is faced with something trying to predict its actions, CDT imagines its decision to not have any effect on its predicted decision.
This means that CDT will only get $1000 in Newcombs problem. If a CDT agent is given the ability to write the code for a new agent, and it expects this new agent to face Newcombs problem, then CDT will write a Son of CDT agent.
To a Son of CDT agent, the moment its code was outputted from the CDT agent is a special moment of magical significance.
If Omega examines a Son of CDT agent, and then plays Newcombs problem, then Son of CDT will 1 box. However if Omega examined the CDT agent, and used that info to predict the Son of CDT agent that would be produced, then Son of CDT will 2 box.
When CDT makes its decisions, it only thinks it controls things causally downstream of its actions. UDT by contrast, is choosing as if it controls every part of reality that is logically correlated with its actions. This allows it to acausally bargain across the multiverse. Son of CDT is somewhere in the middle. It acts as if it controls only the things logically correlated with its actions that are causally downstream of its creation.
If a Son of CDT agent goes on to create further agents, all of those agents will have the same magic moment. They will all care about whether or not Omega's knowledge of them is causally downstream of the moment the moment the CDT agent first wrote code.