I'll take a swing at this, but I'll also flag it to /u/qhapaqocha's attention. Always great to read that redditor's answers!

The Inca built their empire, which they called Tahuantinsuyu "The Four Quarters of the World," with every intention of expanding out forever. In fact, each Sapa Inca (Emperor) had to add new lands because he inherited very little of his predecessor's estate. After death, a Sapa Inca was mummified and a death cult known as a Panaca continued to hold a court for the mummy and rule over that mummy's estate for him in perpetuity. Each Sapa Inca was expected to build his own wealth that his Panaca would one day rule for him.

But I'm getting ahead of myself. It's probably worth saying the Inca started out as just a regional power in and around Cuzco, and it was only beating back an invasion by a powerful foe, the Chanca, that prompted the Inca to expand. You could say they were pushing out their frontiers after that for defensive purposes, but I think it's probably more accurate to say the prince who seized power from his father and led the Inca to successfully defeat the Chanca felt the need to continue to demonstrate his martial prowess to consolidate power at home, keep his army busy, and to extend the reach of the kingdom that he now ruled. Probably everything we know about the Inca's religious justifications for expanding their empire would have been invented around this time.

Even then, the Inca seem to have had some hesitations about entering into a war with the Kingdom of Chimor, the large coastal power whose capital was at Chan Chan. There is a bit of a muddled explanation for how the Inca ended up in conflict with the Chimu —It seems an Inca general attacked a Chimu ally without orders while trying to save face about a mass desertion, so understandably the Inca descendants were not keen to share the story in detail with Spanish chroniclers— but once they were in it, they were in it to the bitter end. Again, we do not have a clear picture of the war, but it lasted years, and when it was done, the Inca denied all Chimu and their coastal allies the right to keep or train with weapons (thus also eliminating one-third of Tahuantinsuyu's manpower from possible military service), but allowed them to keep wearing ear plugs (a status symbol otherwise reserved only for Incas and Incas-by-privilege), albeit the Chimu plugs had to be made of wood.

Anyway, after beating the Chimu, most of the rest of the tribes along the coast of what is now modern Peru joined Tahuantinsuyu without fighting, and now we can start talking abut Imperial expansion as government policy rather than a series of escalating unplanned territorial wars.

The Inca as a rule always approached the rulers of their neighbours first. "Join us and you will retain your rank and station ruling over your people. Your succession laws, local customs, and religion will all be honoured. We will give you women and rich gifts. We will build storehouses and reorganize your agriculture so your people will never go hungry again. We will build royal roads so your neighbours can never invade you for fear of our armies coming for them. We will do all of this if you just join us and allow us to do for you and yours what we have already done for so many other tribes."

And many tribes did join. Joining was a lot easier than going to war, and subjugation was not particularly burdensome for the elite. The Inca kept their word. The local rulers were maintained in place and slotted into the appropriate Inca bureaucratic hierarchy. Meanwhile, their sons and heirs were taken back to Cuzco to be educated as Inca, and the idols of the local Gods were also taken back to Cuzco where they were honoured and feted as passionately as they would have been at home. Keep in mind, of course, on the first word of rebellion, the idol would be smashed or burned and what was left would be scattered over a llama pasture. The Inca literally kept their subjects' gods hostage against their good behaviour.

On the other hand, sometimes tribes refused —especially the martial ones— and then the Inca came for them with all their might and patience and brilliance for bureaucracy translated into that most difficult of military sciences: Logistics. The Inca could keep tens of thousands of men in the field for years, even rotating soldiers home and replacing them with new ones as their tax labour quotas were completed. The Inca were masters of siege warfare. They did not have siege equipment the way European armies did, but they could both starve out an enemy and storm a hillfort. I have read Inca history extensively, and I cannot recall them ever losing a siege given enough time. Upon winning the war, many of the conquered people would be picked up and moved to live somewhere else in the empire, and their lands would then be occupied by colonists from a land long loyal to the Inca.

By the time the Spanish arrived, the Inca frontiers were basically where it was not worth conquering any further. The southern edge of Tahuantinsuyu was the Maule River. The Mapuche lived on either side of the River, but the Inca decided it was not worth conquering the entire tribe, so the Mapuche would qualify as the first of your buffer cultures, if you like. To the north the Inca made it into southern Colombia before stopping. The whole of what is now Ecuador was a rebellious territory for them, and the northern edges were made up of groups so poor they were not actually a net gain for Tahuantinsuyu's economy. There is a story recorded that probably is not true that the Inca actually asked these people to pay their taxes in lice plucked from their own bodies because they had nothing more valuable to offer, and at least that would train them to pay taxes while improving their hygene. Anyway, I expect the Inca would have continued moving north eventually once Ecuador was sufficiently pacified had the Spanish Conquistadores not arrived, but as of the 1530s the northern frontier was where the tribes became too poor and on the far side of rebellious tribes to be worth going further.

As for the eastern border? The Inca did very well in the Andes, but descending down into the rainforest was problematic for them. They did succeed in bringing some groups into Tahuantinsuyu through diplomacy and military conquest, but several invasions into the jungles failed. The Inca referred to people living beyond their eastern borders as mana apuyoc, "Men without a leader." It's tough to negotiate with people who don't even have someone who can speak for the whole group. As long as the Inca got the jungle products they wanted through trade, there did not seem to be a great appetite to subjugate people who could just retreat into the forest forever while shooting arrows the whole way.

So now we get to your 'buffer culture' question in earnest. I guess the answer is yes there were people between the Inca and what the Inca thought of as mana apuyoc, but the Inca did incorporate those people into Tahunatinsuyu as well. The Chacapoyas, The Cloud People who lived on the eastern slopes of the Andes as they descend into the Rainforest, would be an excellent example of these kinds of groups who were organized enough to have a leadership the Inca could engage with, but also through geography and culture were very much their own regional power between Tahuantinsuyu-proper and the peoples beyond the frontier.

Sources: As always when I speak of the Inca, I want to highlight just how solid William H. Prescott's History of the Conquest of Peru is as a one-stop collection of all the written accounts (but no archaeology) available to us. It's old, but it is very comprehensive. Other books on my shelves that are definitely worth a read are Terence N. D'Altroy's The Incas, Daily Life of the Incas by Louis Baudin, and The Incas and their Ancestors: The Archaeology of Peru by Michael E. Moseley. I have some others that I could cite as well, but I once had a mod delete one of my posts for mentioning something written for a general audience rather than historians, so I will restrain myself this time.

Edit: Added a comma.