The Rio Grande pueblos were in turmoil after the success of the Pueblo Revolt of 1680. That turmoil was aggravated every time the Spanish came back, and they came back in 1681, 1682, 1684, 1688 and 1692, each time attacking and burning the Tiwa pueblo at Alameda. It didn't help either that the other pueblos assumed that the Tiwa had been friends of the Spanish because the Spanish stopped at Alameda in their retreat from Santa Fe in 1680. Of course, as the Spanish retreated from New Mexico, they took prisoners and loot and burned the pueblos as they were passing through.
Nearly the entire population of Tiwa Isleta was taken south by the retreating Spaniards. Many of those formed a pueblo at Ysleta del Sur (now inside the city limits of El Paso, TX). Some of them escaped and headed back north. Others had escaped earlier and not made the journey south. They banded together with other Tiwa speakers from the middle Rio Grande Valley and made the journey to Tusayan.
In the aftermath of the Pueblo Revolt and after each succeeding attack, whole clans and families left the Middle Rio Grande and made the journey to the Hopi mesas where they hoped to be beyond Spanish control. And they were, for more than 60 years. Then the Franciscans came.
On the Hopi mesas, the Tiwa were allowed to build a pueblo on a northern finger of Second Mesa. They named the pueblo Payupki, River House. Construction began in the early 1680s and continued for about 20 years as new families and clans arrived. The Spanish finally succeeded in reconquering the pueblos in New Mexico in 1696 and that put an end to most people leaving the Rio Grande area. Only the Southern Tewas left en masse after that.
The Spanish authorities in Santa Fe had no interest in sending troops on a long march across the desert to Tusayan, they had enough problems to deal with in New Mexico. The Franciscan fathers, though, they couldn't let it go. So in the early 1740s, a couple missionaries made the trek to find where the missing Tiwas went to and try to convince them to come back. Their timing was good: there was strife happening between the people of Payupki and the nearby Hopi settlements of Mishongnovi and Shipaulovi. The fathers were able to convince most of the Tiwas it was time. By 1780 Payupki was completely abandoned. It has never been reoccupied.
Early on in their time at Payupki, Tiwa potters seem to have been learning from other potters in the area. They got really good at their craft and made a lot of pottery, so much pottery that the ground around their ancient ruin is still littered with pot sherds everywhere. The people of Payupki evolved their own design vocabulary and built on what they learned from the potters of Walpi and Hano. What they left behind was a multitude of new designs that have now been entered into the Hopi lexicon as "Sikyátki" designs, primarily because they were used by Nampeyo of Hano in the late 1800s and early 1900s.
The potters of Payupki also seem to have used a puki similar to that used as a base to work from by many Zuni potters. There's little known about their migration from the Rio Grande Valley to Payupki but it appears that some of them stopped at Zuni for a few years along the way.
It was pretty customary in those days for long journeys to be made between known water sources. Sometimes a group would stop for months, planting and harvesting a crop or two before moving on. Sometimes that stop might be for several years, and they'd build some kind of structure on the spot. Sometimes pregnant women would layover at a pueblo along the way until they were ready to travel again. Sometimes the ritual specialists accompanying a clan migration might be invited to stay somewhere along the way, too.
A big question that comes up in this is what happened to those Payupki potters who made the journey back to the Rio Grande? Those journeys didn't take years. Led back to the environs of Albuquerque by the Franciscan fathers, they were over in a couple months. And then it was years before the folks from Alameda Pueblo were allowed to rebuild at Sandia because as indefensible and uninhabitable as Alameda was, it provided Albuquerque with a good front line of defense against marauding Apaches and Comanches. Sandia was more defensible and was out of that traffic pattern. That happened about a decade before Governor Juan Bautista de Anza took his troops and several cohorts of Pueblo warriors north with him through the San Luis Valley, around Pikes Peak and down the Front Range to Greenhorn Mountain. In the foothills of Greenhorn Mountain they stumbled across a large Comanche war party headed toward New Mexico and were able to virtually wipe out the entire Comanche high command in a couple hours of fighting. The leader of that war party: Cuerno Verde, so named for the buffalo head with green-dyed horns that he wore as a war bonnet. That's where a lot of names local to the area came from.
Neither Sandia nor Isleta pottery has reached that quality or plethora of designs and styles since they left Payupki. Those who left with the Spanish and returned years later didn't fare any better: the Southern Tiwa pottery tradition was essentially broken. But when you see a Hopi pot with a design pattern on a jar that is clearly broken into panels by vertical lines, or by crossed lines in the bottom of a bowl, you're looking at a design pattern pioneered at Payupki.