Apparently, Rovno was just a "rest-stop" for the CZAJNIK family on their travels away from the Tzar.
Previous possible locations for CZAJNIK include "Alexandriya," "Michalovitz," and most probably, "Slavuta." All three towns may have been Poland, Russia, or Ukraine, depending on the date and activities of the conquering armies.
Finally, "CZAJNIK" is probably derived from "KLOTKE," in the family's attempt to "reduce Jewish visability" to avoid Tzarist attentions.