The history that I linked to is American history from the perspective of European immigrants who settled in North America. From the recorded history I linked to, we can see that the French never purchased land from the Native Americans, but merely coexisted with the Native Americans. We can see that the English received the French forts due to negotiations that took place in Europe, and which took several years before the handovers occurred. We can also read that the English, after taking possession of the French forts in Illinois, then afterward purchased land from the Native Americans in 1772 and 1774. Before purchasing Illinois lands, the English made it clear that no Europeans were to purchase land from the Native Americans without approval of the King of England, clearly indicating that the land was still owned by Native Americans. Ownership of Illinois lands passed to Europeans (French, English, Germans, etc are Europeans) when England purchased those lands. So in 1764, the land was Illinois (land of the Native Americans who were called the Illinois).
About the time of the Revolutionary War, a relatively small band of Virginians (about 125), and led by George Rogers Clark, captured the Illinois forts from the English on behalf of the State of Virginia, and thus Virginia also took possession of the newly purchased lands.
As for people in Illinois traveling to the East Coast, it happened regularly during that period. It didn't happen as often as people traveling from East to West, but it did happen. Traders were constantly floating up and down the Ohio river, and Illinois river; occasionally transporting families. Sometimes, families decided to head back East. Either the women were not satisfied with the frontier, or the men had better business opportunities back East. In the 1770s through 1790, the Indians were very violent (estimated to have killed 10% of the settlers), and several families opted to leave the territory. Of course, the Indians had been treated with great disrespect, but they were violent, nonetheless.
Trails across Ohio, Indiana, and Illinois were traversed regularly by French, English, Germans, and Native Americans. It wasn't like the traffic of the Interstate highways, today, but people did traverse back and forth in both directions.
Settlements, in general, did migrate West. But don't mistake this trend as being solely in one direction. And it certainly was not impossible for families to travel back and forth across those distances. Back then, it was normal to walk across country, even if it took a couple years to do it with long breaks between. I walked from Las Vegas to Northern California one Summer, including across the high desert. Walking long distances is very beneficial to one's health, and our ancestors undoubtedly realized that. How else can we explain some of them living into their 90s and 100s? The point is that it is not so big of a deal for families to travel East at any time, or in any place, in history.