Rabbi Yaaqov states on Qiddushin 39b, "שכר מצוה בהאי עלמא ליכא -- reward in this world is lacking." I am intentionally translating this ambiguously. It can be taken to mean "there is no reward" or that there is reward, but it's missing something. This is elaborated in a Beraisa (ibid and at Chullin ):
רבי יעקב אומר
אין לך כל מצוה ומצוה שכתובה בתורה שמתן שכרה בצדה שאין תחיית המתים תלויה בה
Rabbi Ya'akov says: There is no mitzvah written in the Torah that you are given its reward with it without depending on the resurrection of the dead.
בכיבוד אב ואם כתיב (דברים ה, טו) למען יאריכון ימיך ולמען ייטב לך
About honoring parents, it is written, "In order that your days will be lengthened, and in order that it would be good for you" (Deuteronomy 5:15).
בשילוח הקן כתיב (דברים כב, ז) למען ייטב לך והארכת ימים
About sending away the mother bird, it is written, "In order that it
will be good for you and your days will be lengthened" (Deuteronomy
22:7).
הרי שאמר לו אביו
עלה לבירה והבא לי גוזלות ועלה לבירה ושלח את האם ונטל את הבנים ובחזירתו נפל ומת היכן טובת ימיו של זה והיכן אריכות ימיו של זה
For when his father says to him,
"Go up to the attic and bring me chicks!" And he goes up to the attic, sends away the mother [bird], and takes the children, but on his return, he falls and dies. Where is the goodness of this one's days? Where are the lengthening of this one's days?
אלא למען ייטב לך לעולם שכולו טוב ולמען יאריכון ימיך לעולם שכולו ארוך
Rather, "In order that it be good for you"—in the world which is all good; "And in order that your days will be lengthened"—in the world which is all long.
(Interestingly but tangential to your question, one of the storied the talmud gives for why the great tanna Elisha ben Avuyah became an apostate and nicknamed "Acheir -- the Other" was because he saw just this scene -- a son died sending away the mother bird to obey his father's request to get eggs -- and failed to see Divine Justice. Now the more interesting part -- R' Yaaqov was Acheir's grandson.)
So it would seem from this gemara that Divine Justice is at best incomplete without taking people's fate in the World to Come into account.
On the other hand, Rabbi Gamliel the son of Rabbi Yehudah haNasi (Avos 2:5) appears to assume that punishment is in this world:
אַף הוּא רָאָה גֻלְגֹּלֶת אַחַת שֶׁצָּפָה עַל פְּנֵי הַמַּיִם. אָמַר לָהּ, עַל דַּאֲטֵפְתְּ, אַטְפוּךְ. וְסוֹף מְטִיפַיִךְ יְטוּפוּן:
He also saw a skull that was floating on top of the water. He said (to it): "Since you drowned [others, others] drowned you. And in the end, those that drowned you will be drowned.
Would Rabbi Gamliel III have said this if it was possible that in the end, those who drowned the person whose skull he found might be punished in the World-to-Come?
It could be that this is a simple dispute. Or it could be that Rabbi Yaaqov's incomplete recompense in this world would necessarily include being punished for murdering. Or that Rabbi Gamliel meant "drowning" metaphorically -- "those who drowned you will go through their own parallel suffering."
Then there is Nachum ish Gimzo, who said "גם זו לטובה -- this too is for the good" (Taanis 21a) that the other sages punned on the name of his hometown and called him Nachum ish "Gam-zu". And his student, Rabbi Aqiva, declared, "כל דעביד רחמנא לטב עביד -- Everything the All-Merciful does, He does for the good." Meaning, that Hashem acts in this world terms of what will provide the best outcome for everyone involved. This is not always reward or punishment. And so we find Hashem holding off on punishment to give opportunity for teshuvah.
I believe this is what motivates statements like Berakhos 7a "צדיק וטוב לו - צדיק גמור, צדיק ורע לו - צדיק שאינו גמור, רשע וטוב לו - רשע שאינו גמור, רשע ורע לו - רשע גמור -- a tzaqiq and life is good for him is a pure tzadiq; a tzadiq whose life is bad for him is an incomplete tzadiq, an evil person whose life is good for him is not entirely wicked, and an evil person whose life is bad for him is entirely wicked." Or Eiruvin 22a, which says that Hashem will delay on repaying a wicked person for his evil, but not a good person for his infractions.
A righteous person who is in a place where he could learn from his wrongdoing, may be woken up with tragedy in this world. A wicked person, it serves little point.
Each gets what's best for them and for the world. Whether that means delaying punishment or reward until the afterlife, or receiving it in the here-and-now.
