I am intrigued by the Tercentary because I've never heard of another royal dynasty which has celebrated its own accession to the throne like this. I mean, most new dynasties try to stress the continuiation with the former dynasty and thus their legitimacy. Therefore I am puzzled by the Romanovs putting the spotlight on the very fact that Mikhail Romanov was the great-nephew of Ivan the Terrible's first wife and not a Rurikid nor a direct descendant of Alexander Nevsky.
For example I am quite sure that William the Conqueror would not be amused if you suggested that 1066 should be celebrated as the dawn of a new era and the accession of the Rollonids, like we interepret it today. He propagated it as his rightful claiming of his inheritance, as first cousin once removed and designated heir of Edward the Confessor. The accession of William, Prince of Orange, to the British throne as William III, was indeed hailed as a Glorious Revolution and thus a definite break, but of course William himself presented himself as the lawful Protestant heir. The same with the Hanoverians. In these cases religion (and constitutional politics) played a role that you don't find in the Romanov case.
The only comparable examples of the Romanov case must be some German dynasties, like the Hohenzollerns, Habsburgs, Wettins and Wittelsbachs, whose accessions way back in the early Middle Ages were synonymous with the very foundation of the states of Brandenburg-Prussia, Austria, Saxony and Bavaria and as such could be celebrated in the historicizing 19th century. E.g. the Hohenzollern Jubilee in 1915, the Quincentary of the accession of the first Hohenzollern Elector of Brandenburg (1415).
But Russia was there well before the Romanovs entered the scene. I think this "dynastical consciousness" for no explicit religious or political reasons, just for the sake of it, marks the Romanovs as somewhat unique among royalty. Add to this their inofficial use of Romanov as a surname, the official use of the derivation Prince Romanovsky and the use of the family arms (which unlike most other dynastical arms were not territorial!) in the new arms for junior and distant members etc.
That they "dared" to put the spotlight on their own legitimacy like this could of course be interpreted that they were extremely sure of their position, that the mere thought of questioning it didn't even occur to people. But then they did put the spotlight on the first Romanov being elected by a (boyar) duma (and not by the Grace of God), just at the time when they were struggling to uphold autocracy against the new duma. It really is intriguing....