Memorized astrological sequences -like little recitations- would facilitate the sequencing of the ends of the rope/string order of application. Weaving strands could also be done as well as knot tying.
Since these are relatively rare, and literally millions served in the legions over the span of hundreds of years (the end of the Roman Empire didn’t come until 1453, when the Turks sacked Constantinople, a mere 39 years before Columbus set sail for the New World), and knots were used everywhere, I don’t think it was used for that, or for any practical use.
Souvenirs, or perhaps gifts, obtained or presented somewhere they served?