Japan is a mountainous country and isolation between the many settlements in the feudal periods was common. It was not until the regularization of the alternate attendance system by Iemitsu Tokugawa between 1635 and 1642 that a sense of nationalism began to form in Japan among the common people. The alternate attendance system required daimyo to "attend" in the capital of the time, Kyoto, rather than live in domains, so the shogun could keep tabs on them. This was a pre-Tokugawa practice and had roots in the treatment of daimyo by an earlier shogun in the 1300s. The early form of attendance was not ongoing, scheduled, or universal. Iemitsu changed this.
It was a most effective system of political control. All daimyo had to maintain residences in Edo as well as in their home domain. They would attend upon the shogun by residing in Edo in alternate years. Their wives and children had to remain behind in Edo when they went home for a year before their next period of attendance.
The travels of these daimyo spurred the improvement and creation of roads, inns, and a sense of communal space. It should also be noted that during this era, commoners needed permission to travel and were not supposed to move to cities. However, the enforncment of such rules was often quite lax. The daimyo began fueling urban growth by pulling their samurai followers into semipermanent garrisons in castle towns. This brought the roads teaming with life, and created in infrastructure of transportation and communication. Travel became so common that maps and guidebooks were produced.
To answer your question, it wasn't until the twilight years of the feudal Tokugawa Period (the second half of the 19th century) that Japanese people really had a widespread sense of "Japaneseness" due to the presence of Western powers and their insistence on trade and globalization.
In regards to "seeing themselves as being from separate nations" that was hardly the case. The standard education of Confucianism at the time reminded of the Japanese people's origin from China, however they were not Chinese. They were uniquely Japanese. This view was propagated even more by the Mito School of learning with Nativism; which taught that Japan was uniquely blessed and formed by the sun goddess Amaterasu. No other nation (namely China) was of her august children like Japan.
sources:
Gordon Andrew, A Modern History of Japan from Tokugawa Time to the Present Third Edition. Oxford University Press: 2014. p 15-42
Motoori Norinaga, "Sekai Daishiso Zenshu (Complete Works of Great Thoughts of the World)", Vol 54 Nihonshiso-hen (Japanese Thought) Tokyo: Shunjusha, 1972 p 17-21