Hungarians Conquested the Carpathian basin in the 9th century. the nation was forged together by the strongest tribe, the magyars. Szeklers are a magyar tribe, and they settled in Transylvania after the conquest.

the gap between the Szeklers and Magyars on the map is the result of more hundred years of conquests and wars. the Mongol Invasion destroyed many of the magyar settlements in the Kingdom of Hungary, so did the Ottoman Invasion, and the Habsburg rule. those effects were the shift in culture and change in the ethnical compilation of the population in the region. mainly romanians from Wallachia moved in to repopulate the empty settlements after the 13th century.

as the effect of the peace treaty of WWI, KoH lost 64% of its population and 72% its trerritories. 31% of the magyar population was left outside of post-war Hungary. the biggest magyar population was attached to Romania.

note, the szeklers might look separated, but they have a strong magyar identity and use magyar language, and magyars consider them magyars. you can surely accuse modern romanians for the forced assimilation practice of the past fourtyfive years, but the attenuate started in the 13th century.

Was Transylvania settled by Hungarians after parts of modern-day Romania were conquered?

yes. maybe even a few hundred years before the conquest.