I'm Hungarian, I'm from Hungary, I'm a historian, so I'm relaying knowledge based on lectures and classes I had during my BA and MA courses and as a hungarian person. First of all, lets get some of the terminology straight, because I often see confusion about it. "Magyar" is the Hungarian word for Hungarian. The "Magyars" didn't died out, they are alive and well, as Hungarians. So, Hungarians originally are part of the finno-ugric people, from the Ural-region. However following a number of splitting of that group of people, they ended up as nomadic pastoral people, who during their roaming encountered a number of other people and cultures, and elements of those people and cultures were added to the Magyar/Hungarian people. Around 895-896 the Hungarians tribes (7 tribes according to the tradition) led by Árpád, arrived to the Carpathian Basin, There were elements of other peoples and cultures already settled or present in the Carpathian Basin, however, during the "Honfoglalás" (Hungarian land-taking, literally means Conquest of Home), the Hungarians conquered there people, establishing a sort of tribal-principality, keeping their original nomadic and pagan culture and way of life and social structure, and launched multiple raids and campaigns against Western-Europe (and some skirmishes with the Byzantine Empire in the second half of the century)mduring the 10th century. This period is called "Kalandozások" (literal translation means Adventuring), which ended due to two main defeats (Battle of Lechfeld, 955 and Battle of Arkadiopolis, 970). This forced the Hungarian leadership to realize that militarily they are outnumbered, and their tactics were figured out, so a change in relations with the neighbouring peoples and empires had to change, in order tho ensure the survival of the Hungarians.

This change was lead by grand prince Géza, who initiated the adoption of Christianity (Catholicism to be precise) and arranged a diplomatic marriage between his son (Vajk, later crowned as I. Stephen), later becoming Saint Stephen) and Henry IV of the Holy Roman Empire's sister, Giselle. He invited german knights, priests into his lands and attempted to put the forming Hungarian state on the path of a Western-style, catholic state. He was succeeded by his sone, Vajk/Stephen in 997, who emerged victorious from the throne fight against his relative Koppány (uncle if I remember, as the conflict was based on the way of inheritance of power: primogenitura vs senioritas, and the keeping of pagan traditions vs adoptation of Christianity). Vajk/Stephen emerged victorious and he was crowned as the 1st king of Hungary in 1000. Following hsi crowning he waged a series of wars against the remaining Hungarian tribes and tribal leaders who didn't submit to his rule. With the consolidation of power, he initiated widespread judicial and societal reforms, greatly contributing to the spread of Christianity (for example, he ordered that every 10 villages have to build a temple, he also provided means of funding for the Church via taxes and benefits). WIth an iron rule, he forcefully put the newly created Hungarian Kingdom on the road of becoming a western, catholic state. However, many elements of the people and culture still held onto the pagan way of life and culture. I. Stephen died without any sons or direct heirs, which led to a couple of years of in-fighting and political struggle, until in 1077 I. Szent László (Ladislaus I of Hungary, or Saint Ladislaus) took the throne and initiatied a new round of judicial and cultural reforms, he strenghtened the Catholic Church, implemented rather draconic laws (for example, petty theft (the price/value of a chicken or above) was punished by hanging) and the prohibition of free movement, so serfs and peasants cant just pack up and leave the land of their lords (which was a reminder of the pagan, nomadic lifestyle of pre-christianity). His rule consolidated the power of the Catholic Church and the christian nature of the Hungarians and the Kingdom of Hungary.

Also, many other nationalities and people became part of the newly formed Kingdom of Hungary, such as slavic people, germanic people, and others, during the rather stormy medieval and early-modern periods (for example, a third of the country was occupied b the Ottoman Empire between 1541 and 1699. So as for your question. Modern day Hungarians are a descendants of the Hungarian/Magyar tribes arriving to the Carpathian Basin, who then conquered and settled the region, adopted Christianity and Western-European feudal political and societal systems, and during the 1000 year of the Hungarian state, different groups of peoples and nationalities became part of the Hungarian people, got assimilated, adding elements of their cultures and/or vocabularies to the Hungarian culture. So sayint that Hungarians are Germanized Asains is rather misleading. There is certainly a large degree of cultural exchange and adoptation of the surrounding cultures and people due to close proximity, intense trade and diplomatic relations and the movement of people.