I believe this might be because of the random media query string used, when the search instances are saved and the CSS files are re-generated. WP Rocket is probably saving the files individually, detecting the media query string as well.
If you make changes to ajax search pro, just make sure to clear the site cache as well, and these files should be deleted I guess. I don't think this is actually an incompatibility, simply the WP Rocket cache was uncleared.Best,
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