If a person does not realize that he had a wet dream until the end of the day – what should he do?

Yes, what you did was correct and in accordance with
sharee’ah. Purity is a condition of prayer being valid, and janaabah
necessitates ghusl. The prayers that you offered whilst junub are excused
because you did not do that deliberately, but you did not discharge your
duty after you realized what your situation was until you did ghusl and
repeated the prayers. This is what you did and this is correct. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked
about someone who noticed semen on his clothes after he had prayed Fajr, and
he had not noticed it before. What is the ruing on that? 

He replied: 

If he did not go back to sleep after praying Fajr then his
Fajr prayer is not valid because he did it when he was junub, as he can be
certain that it happened before he prayed. 

But if he went back to sleep after praying Fajr, then he does
not know whether this happened during his sleep after the prayer or during
his sleep before the prayer, so the basic principle is to assume that it
happened after the prayer and that the prayer is valid. The same ruling
applies if a person notices traces of semen and is not sure whether that is
from the previous night or the night before that, so he should assume that
it is from the previous night and that it happened in the last period of
sleep, because that is more certain, whereas there is some doubt concerning
what came before that, and if there is doubt concerning something that
invalidates one’s state of purity there is no obligation to purify oneself
from it. The Prophet (S) said: “If one of you feels something in his stomach
and is not sure whether something (i.e., wind) came out of him or not, then
he should not leave the mosque.” Narrated by Muslim from the hadeeth of Abu
Hurayrah (may Allaah be pleased with him). And Allaah is the Source of
strength. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen,
11/question no. 165. 

The Shaykh was also asked: 

A person prayed Maghrib
and ‘Isha’, then he went home. When he took off his clothes he noticed
traces of semen on his underwear. What should he do? 

He replied: 

If this man who found semen on his clothes did not do ghusl,
then he has to do ghusl and repeat the prayers that he offered when he was
junub. But sometimes a man may see traces of janaabah on his clothes and not
know whether that happened the previous night – should he regard that as
having happened the night before or on a previous night? 

The answer is that he should regard it as having happened on
the night before, because there is some doubt concerning the previous night,
so the basic principle is that he was in a state of purity (on the previous
night). Similarly if he went to sleep after praying Fajr then woke up and
noticed traces of janaabah on his clothes, and he does not know whether that
was from his sleep after Fajr or his sleep during the night, should he
repeat Fajr prayer? 

The answer is that he does not have to repeat Fajr prayer,
because there is no certainty that he had a wet dream whilst he slept during
the night. So you should make this the rule you follow: every time you are
uncertain as to whether this janaabah happened during a previous sleep or a
later sleep, assume that it was during the later sleep. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen
(11 Shawwaal, no. 166). 

And Allaah knows best.