Albert Barnes Commentary Exodus 40:20

"And he took and put the testimony into the ark, and set the staves on the ark, and put the mercy-seat above upon the ark:" — Exodus 40:20 (ASV)

The testimony – that is, the tables of stone with the Ten Commandments engraved on them (Exodus 25:16; Exodus 31:18). Nothing else is said to have been put into the ark. These were found there by themselves in the time of Solomon (1 Kings 8:9; 2 Chronicles 5:10). The pot of manna was laid up before the testimony (Exodus 16:34); Aaron’s rod was also placed before the testimony (Numbers 17:10); and the book of the law was put at the side of the ark (Deuteronomy 31:26).

The expression “before the testimony” appears to mean the space immediately in front of the ark. Most interpreters hold that the pot of manna and Aaron’s rod were at first placed between the ark and the veil, and afterward within the ark (Hebrews 9:4). It is very probable that the pot and the rod had been put into the ark before it was taken by the Philistines, but that they were not sent back with the ark and the tables (1 Samuel 4:11; 1 Samuel 6:11).