1. Rashbam’s language and Rashi’s language here seem very similar but there is a subtle difference between them. Rashi suggests that the two three-tribe units mentioned before vs. 17, the one led by Judah and the one led by Reuben, would always travel first, followed by the Levites and then followed by the other two three-tribe units. Note Rashi’s language: ונסע אוהל מועד: לאחר שני דגלים הללו. Rashi’s position seems to be the simple meaning of the phrases at the end of vss. 9 and 16: “These shall march first” and “these shall march second.”
Rashbam, on the other hand, says that the order was always: two unspecified three-tribe units would travel first, followed by the Levites and then followed by the last two three tribe units. As Rashbam’s comment continues, the logic of his position and the importance of the distinction become clearer. See note 17.

2. In other words, the three-tribe unit that was to the east when the Tabernacle was encamped would always be to the east when they were traveling. So also for all the other three-tribe units.
See P.T. Eruv. 5:1 (cited by Rashi ad 10:25, below) where there are two opinions about the pattern of the placement of the tribes when they were traveling. One opinion says that they traveled in formation, with Judah always in the east and Reuben always in the south and so forth. Our verse “as they camp so shall they march,” is the prooftext used to establish that opinion. Rashbam clearly follows that understanding, not the opinion in P.T. there that the tribes traveled in a straight line. (Cf. e.g. Luzzatto ad 10:14, who is certain that the tribes must have traveled in a straight line, not in formation.)
Now the logic of Rashbam’s previous comment becomes clear. The “Judah” unit, he argues, always has to be to the east (vs. 3) and the “Reuben” unit always has to be the south (vs. 10). Then Rashi’s claim – that those two units were always the ones that traveled first – does not make sense (unless the tribes always traveled in a south-easterly direction). Rashbam says instead that, depending on the direction that the Israelites were to move, whatever two three-tribe units ought to be traveling first, did so. This was done in such a way that the unit to the east always stayed in the east, and so forth.
Rashbam does not tell us how he would explain the phrases “These shall march first” and “These shall march second” at the end of vss. 9 and 16. Nor does he comment on 10:5–6 or 10:11–25 where again the simplest explanation is that there is a set order of travel for the tribes, rather than a set position for each tribe in the camp as it moved. One can only speculate that he understands these phrases as the instructions for the first time that the camps moved. In future travels, the order would be determined by the direction traveled.

3. Rashbam continues to dispute Rashi’s claim that the order in which the three-tribe units were listed is the order in which they always traveled. Rashbam says that the order is simply the natural order that one would expect from a biblical text: the narrator begins by facing east and then turns clockwise (“to the right”).
The Talmud often suggests that the “normal” order in the Temple is that one begins by facing east and then moves to the right. See e.g. Yoma’ 15b.
The dispute between Rashbam and Rashi here (does the order of listing reflect the required order of travel?) follows the same pattern as the dispute between them in explaining the phrase (Gen. 28:12), “angels of God were going up and coming down on it.” Rashi feels that the order – first going up and then coming down – must say something about the order in which the events occurred. Rashbam, on the other hand, says that standard style dictates writing “going up” before “coming down.”