Despite history of united Spain and Russia counting several centuries, there was only one war officially waged between the two and it was more like a curiosity than a proper conflict. It was called Russo-Spanish war and lasted for two years from 1799 until 1801. It was triggered mainly by the Spanish leaving the Coalition and allying themselves with Napoleon. There were a lot of heated diplomatical letters sent by both parties to each other, but no military engagement ever took place and Russo-Spanish American relations soon become somewhat more cooperative, although many Russian officers and administrators in America were concerned it would've been hard for them to repel possible enemy attacks due to extremely small garrisons deployed there.

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I am unaware of any real tensions between both countries in described period, but maybe some other users can contribute more to this topic.

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Sources:

Milyutin A., "History of war of 1799 between France and Russia";

Leonty Bennigsen, collection of published letters from "Istorichesky Vestnik", 1917.