Not very funny one. The astrologer says only that he won't be able to produce any more children in the future. There is the implication that the kids might die and he will be childless as the initial prediction implies.
I took it to mean that the astrologer is bad at his job and shifts the goalposts so he’s “right”, like “you won’t have any more kids AFTER THIS!” As psychics and astrologers have been known to do for thousands of years apparently.
Yes, I agree. In those situations the usual punchline is "I hope that you will take care of them as if they are yours." and that's why I didn't think of that interpretation.