Firstly, if semen comes out during the day after intercourse at night, that does not invalidate the fast. We have been permitted to eat, drink and have intercourse from sunset until dawn comes. Allaah says (interpretation of the meaning):
“It is made lawful for you to have sexual relations with your wives on the night of As‑Sawm (the fasts). They are Libaas [i.e. body-cover, or screen, or Sakan (i.e. you enjoy the pleasure of living with them)] for you and you are the same for them. Allaah knows that you used to deceive yourselves, so He turned to you (accepted your repentance) and forgave you. So now have sexual relations with them and seek that which Allaah has ordained for you (offspring), and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night)…”
The scholars (may Allaah have mercy on them) have stated that if semen comes out during the day after having had intercourse at night, that does not invalidate the fast.
It says in al-Jawharah al-Nayyirah (1/138), which is a Hanafi book:
If a person who is having intercourse fears that dawn will come so he withdraws, then he emits semen after dawn, that does not break his fast. End quote.
And it says in Haashiyat al-Dasooqi (1/523), which is a Maaliki book:
If a person has intercourse at night and his semen is emitted after dawn, it seems that he does not have to do anything, as is also the case for one who puts on kohl at night then it reaches his throat during the day. End quote. It says something similar in Sharh Mukhtasar Khaleel, 2/249.
Al-Nawawi, whose madhhab was Shaafa’i, said in al-Majmoo’ (6/348):
If a person has intercourse before dawn then he withdraws when dawn comes or straight after it comes, then ejaculates, that does not invalidate his fast, because it came as the result of permissible intimacy, so he does not have to do anything. The same applies if a man’s hand is cut off in a case of hadd punishment and he dies as a result (i.e., no one is responsible for his death). End quote.
If a person has intercourse then does ghusl, then some semen comes out of him after doing ghusl, he does not have to do ghusl again, because the reason for that is one reason, so there is no need to do two ghusls. Rather he has to do ghusl if he ejaculates again as the result of renewed desire.
And Allaah knows best.