Most are compression fit with tabs that fit inside the chimney flue, or that tighten over the outside of the flue extension. You only want it tight enough to prevent it from being dislodged by wind. Do not drill the tiles, tighen if, and as necessary to create a compression fit, but as you noted, not so tight as to crack the tile.

Chimney caps are sold in sizes to fit specific flue openings. It should be a close fit to start with, and the bolts serve to adjust for small variations within the size you purchased, and to prevent wind throw.