There was no conflict, per se, between Zapata & the US, nor was Zapata a 'nationalist'.
Mexico, traditionally, has been a very provincial, very regionalist "nation". Much like pre-WW1 US, Mexican nationals tended to reside in the towns & areas where they were born. Under the Spaniards, and then after independence, locals were largely concerned more with local issues than national ones. Part of the reason there was a break with Spain began over 100 years prior to the call for independence, when the Spanish Bourbons enacted reforms which would tighten the Imperial (and later national) government's control & involvement with local affairs, largely on the side of those who were landed or of means.
Zapata's contention was that the local landed gentry, the hacendados or hacienda owners, had swindled the local peasantry of the communal lands, some of which had been held in communal ownership since the time of the Spaniards in the 1600s - 1700s. With the cooperation of the national government & legal system, ownership of the lands had been passed to the gentry, in essence creating a kind of serfdom in Morelos, the state in which Zapata's hometown resided. Zapata's campaign was principally to restore ownership of the lands to the peasantry. His armies principally operated in Morelos with only the occasional excursion into the State of Mexico to the north.
Villa, operating in far northern Mexico, was, again, more regionalist than nationalist although he, like Zapata, realized that national leaders needed to be more sympathetic to Mexican nationals than simply a rubber stamp to foreign interests. In Villa's case, he, like Zapata, was interested in the affairs of his home state (in Villa's case, the state of Chihuahua). Yet he, unlike Zapata, fought over a wider range of national territory to have a more democratic leadership installed in the capital. Once the initial phase of the revolution was over (i.e the ouster of Mexican dictator Porfirio Diaz &, later, his equally despotic successor Victoriano Huerta), Villa returned to Chihuahua.
For much of the Revolution, Villa did not have issues with the United States. More often than not, he guaranteed the safety of American nationals, and actively courted American recognition of his importance in the revolt. However, his friendship towards the US ended when Villa's fortunes fell & his armies were destroyed in the civil war that marked the 2nd phase of the Revolution. Without the backing of his armies, support by the US for Villa fell, & it was given, instead, to Villa's opponent Venustiano Carranza. At which point Villa initiated a campaign whereby he allowed his lieutenants to regularly make raids across the border, attempting to entice the US military to invade Mexico. He hoped this invasion would bring the US into conflict w/ his nemesis Carranza, and regain him his old stature in the eyes of the Mexicans.
In either case, neither saw a direct conflict between Mexico and the US. They did not favor the Mexican government's eagerness to grant excessive rights to Mexican resources, yet unless that affected their localities directly, it was not an immediate conflict.
Emiliano Zapata - John Womack
The Life of Pancho Villa - Fredrich Katz
The Wind that Swept Mexico