This answer will need significant expansion to cover all 18 Legions. But yes, certain aspects of a Legions character were already fixed in alignment with their Primarch's fate, even before the Primarch was found by the Emperor.
V Legion : White Scars
. Their early experience in pioneering and scouting also saw the Star Hunters master the art of hit-and-run and maneuver warfare that would come to define them in the future. Soon enough the Star Hunters were known not only as pioneers but also as raiders who struck swiftly and without warning.
The hit and run tactics favoured by the Star Hunters prior to their reunion with their Primarch Jaghatai Khan mirrors the hit and run tactics used by The Khan in the defeat of the Palatine's Empire by the tribes of Chogoris and the future White Scars they would become.
Initial recruits for the Star Hunters were drawn from the ice wastes of the Thulean Basin. While this isn't a duplicate of the region of Chogoris that Jaghatai was raised on, the barren grasslands of the Empty Quarter and the Icelandic wastes share many similarities in the difficulties they pose towards those living there.
VI Legion : Space Wolves
Before the coming of their Primarch Leman Russ, the Space Wolves were known as the VI Legion and was made up of a diverse range of savage and hyper-violent tribesmen from Terra.
The background of the VI Legion is a strong match for the savage tribes of Fenris where Leman Russ is found, and eventually becomes the chapter's homeworld.
VIII Legion : Night Lords
Originally known as the VIIIth Legion, the Night Lords first recruits were from the stinking ancient prisons of Terra. Here the children of prisoners were raised in the dark and among death. These pale "Night's Children" made perfect Astartes recruits.
This is uncannily similar to Konrad Curze background on the lawless hive planet Nostramo.
XV Legion: The Thousand Sons
Five years into the Crusade however, the warriors of the legion – much to their delight - all began to spontaneously develop psychic abilities.
Over the next several decades some of the then-discovered primarchs found the notion of psychic mutants being allowed to exist as part of the Emperor's Crusade distasteful at best...
It was shortly after this that the Great Crusade arrived at Prospero and found Magnus...
The Thousand Sons Primarch is of course, Magnus the Red, found on Prospero, a world of outcast human psykers, where Magnus' own psychic abilities were allowed to grow and florish.
XXth Legion: Alpha Legion
Like the Salamanders and Space Wolves, the XXth Legion was formed and established largely in separation from the rest of the Legiones Astartes, likely for a very specific purpose. These three specific legions were obliquely called by some sources as "Trefoil".The earliest known activities of the legion saw it conduct abductions, targeted strikes, and assassinations to the Imperium's enemies on Terra and beyond.
While the "secretive" birth that the Alpha Legion shares with its mysterious Primarch, is shared by two other Legions. The role it expanded into enhanced this secrecy more than was true for the others. Alpharious's story does not include a home planet, but his first encounter with the emperium was marked by similar tactics of a small force vs a more numerous foe;
Using a ragtag fleet of primitive one and two-man fighters he cleverly put the advance ship of the Luna Wolves' fleet in a precarious position, which necessitated the intervention of Horus himself.
The XXth's signature methods fit perfectly with their Primarch's approach to warfare.
Alpharius quickly developed a unique approach to Astartes operations, focusing on the philosophies of initiative and flexibility, as well as extensive use of subterfuge and non-Astartes specialist operatives.