My daughter is Crimean Tatar. I mean, if you want to be even more technical, Tatars are a Turkic tribe originating from the Altai to Mongolia. But they were certainly the majority population for centuries. Before that it was other people, non slavic, such as Greeks. (Stalin got rid of the remaining Greeks too).

The Second Russo-Turkish war enabled Russia to claim Crimea but it had one mighty big caveat. In the treaty of Paris it was implicit that the Black Sea was to be demilitarized and that there was to be no Navy base in Crimea. Russia broke that agreement within 5 years and has been in breach of it ever since-making its entire claim to Crimea moot.

The rest, as you said, is by ethnic cleansing and importing a Russian population.

but the fact also remains that the Tatars were and are strongly opposed to Russian rule and control and fine about Ukranian rule and control. And right now most of their political and religious leaders are in jail.

Lastly, Russia agreed to Ukraine's borders when Ukraine gave up its nuclear weapons and guaranteed to protect them. So Russia, again, has simply no claim on Crimea.