Joseph asked his family to take his bones back to the promised land when they returned:
Then Joseph made the sons of Israel swear, saying, “God will surely visit you, and you shall carry up my bones from here.” (Gen 50:25)
When Moses led the people of Israel out of Egypt, he did take Joseph’s bones with him (Exo 13:19) and these were eventually buried in Shechem (Jos 24:32).
Earlier, the body of Jacob (Joseph’s father) had been taken from Egypt and buried in Machpelah (modern Hebron) in Canaan (Genesis 50:5,13-14).
Josephus (Antiquities, ii.8.2), writing in the first century AD, says that the same thing happened with Joseph’s brothers:
At length his brethren died, after they had lived happily in Egypt. Now the posterity and sons of these men, after some time, carried their bodies, and buried them at Hebron: but as to the bones of Joseph, they carried them into the land of Canaan afterward, when the Hebrews went out of Egypt, for so had Joseph made them promise him upon oath.
Presumably this was based on a tradition that was known in the first century.
Stephen summarized the above three accounts in his speech when he said
And Jacob went down into Egypt, and he died, he and our fathers, and they were carried back to Shechem and laid in the tomb that Abraham had bought for a sum of silver from the sons of Hamor in Shechem. (Acts 7:15-16)
This is typical of New Testament narratives in conflating several separate events into one.
So to answer the question, most likely the bodies of Joseph’s brothers were buried in Canaan, but before the Exodus and not at the same time as Joseph.