It's not that Germans considered Czechs to be German, it's that Germans considered most of Bohemia (half of the Czech Republic today) to be German. The reason is that these lands were German in addition to being Czech -- they were multi-ethnic. And since Bohemia was a part of the Austrian empire, it was dominated by ethnic Germans. For a time, Prague (the Czech capital) was a German city, i.e., German was the primary language spoken in Prague. The Czech nationalist movement countered this in the eighteenth century, and by the time of World War I, Prague had become a Czech-dominant city once again. Nevertheless, when Czechoslovakia declared its independence in 1918, Bohemia still maintained an enormous German minority of millions, so much so that one if five citizens of Czechoslovakia was German as the Second World War approached. Ostensibly, it was because of this large German minority that Hitler demanded that the other powers of Europe cede to him a large portion of Czechoslovakia in 1938. After England and France (but not Czechoslovakia) agreed to his demands at the infamous Munich Conference of 1938, Hitler subsequently invaded the remaining ethnically-Czech portions of Czechoslovakia, thus revealing his true intentions (i.e., to obtain Czech industry for Germany). And, yes, this does have something to do with your question, because in 1945, after Nazi Germany's defeat, Czechoslovakia expelled millions of Germans from Czechoslovakia, and this is the reason that we no longer see a large German minority in Bohemia (for the remainder of the twentieth century, to stay within the rules of the subreddit).

Aren't you approaching this a bit backwards? The Czechs weren't German - but they lived in a huge state (the Austrian Empire) which was a part of the Confederation...

The Czech people were not considered German, but today's Czech Republic is more or less territorially the same as the old Kingdom of Bohemia, which crown was held by the Austrian Emperors. At the time of the map you link, Bohemia was politically and culturally German despite much/most of the population being ethnically Czech. Bohemia had been part of the Holy Roman Empire for centuries before that, as well, under German lordship.

Another factor is that although the population was primarily Czech, there was nonetheless a large German population in Bohemia until WW2, which was one of the justifications used by Hitler to annex a portion of Czechoslovakia (specifically the Sudetenland province which bordered Bohemia).

Although the makers of the German Confederation acknowledged some inkling of the national principle, for the purposes of boundaries and other sundry details, hard realpolitik factors tended to triumph over ethnic demographics. The two main powers in the Confederation, Austria and Prussia, had a somewhat fractious relationship that long predated 1815. Although they were the two guarantors of the Confederation, each side was looking to gain advantage over the other in the negotiations over the Confederation. For instance, one of the Prussian proposals eliminated Bohemia from the planned Bund and had a truncated Austria as territorial components of the Confederation. Such proposals were a dead letter in Vienna, and Metternich pushed that both the crownlands and Bohemia be considered integral components for the Confederation.

Although the sizable German-speaking minority in Bohemia was a good pretext for the region's inclusion in the Confederation, the underlying rationale was geographic. Bohemia had been one of the main locii of Austro-Prussian military conflict since the Silesian Wars of the eighteenth century and the recent Napoleonic Wars had underscored the importance of the region's passes to military operations. If Austria and Prussia had come to blows, it was more than likely to come in Bohemia, so Metternich pushed for the inclusion of Bohemia in the Confederation so that any Austro-Prussian conflict would become a matter for the German Confederation. There was a similar logic to having the duchies of Zator, Oświęcim and Żywiec also included in the Confederation despite their nominally German population. These cities were adjacent to the strategically important Free City of Krakow and Austria feared both Prussia or Russia would seize this fortress town and open up the Empire's eastern marches to invasion. The Duchies thus acted as a tripwire to ensure that Confederation would respond to any aggression against Krakow. Bohemia likewise emerged as a means to check Prussian aggression. The smaller German states also preferred Bohemia to be included in the Confederation because it was in their interests to have a strong Austria counterbalance Prussia and thus leave "Third Germany" in relative peace.

The problem of an ethnically mixed Bohemia came to a head in the Revolutions of 1848. The Czechs and Germans in Bohemia soon came to loggerheads after the initial revolutionary wave of enthusiasm died down. The German convention in Frankfurt am Main had invited Bohemia to send a delegation to Paulskirche as part of the settling of the German question, but this move opened up political fissures both in Bohemia and the Paulskirche parliament. Pro-Bohemian factions in the Paulskirche argued that the German minority was the driving force in the the region's economic and cultural spheres and pushed for Bohemia's inclusion as a Germanic territory despite the presence of so many Czechs. This, however, opened up the issue of equal rights for Slavic-speaking peoples,and was one of many contentious issues about a future German state that the Paulskirche did not resolve. Inclusion in a future German state was far from uncontentious in Bohemian politics as well. German liberals in the Sudetenland and Prague took up the Paulskirche's offer to send delegates to the Parliament, but the Czech nationalist activists boycotted the May 1848 elections to the German National Assembly and instead organized their own Slavic congress in Prague. When the Prague garrison commander Prince Alfred Windischgrätz dissolved the Slavic congress by force in June 1848, the Paulskirche Assembly congratulated Windischgrätz for his German victory over Slavism, even though Windischgrätz's actions were a sign that the forces of Reaction had caught their breath and would soon try to stamp out the Revolution in Germany.

So the overarching lesson of this Bohemian affair is that the national composition of Bohemia initially was not that important to the German Confederation's borders. Raison d'État was much more important for the boundaries of this new entity than creating an ethnically homogeneous state. The national principle though grew in importance in the decades after 1815 and thus Bohemia became an contentious issue in Central European politics with some German nationalists considering the region intrinsically German and Czech and other German activists steadfastly disagreeing.

Sources

Kraehe, Enno E. Metternich's German Policy. Volume II. Princeton: Princeton University Press, 1983.

Vick, Brian E. Defining Germany: The 1848 Frankfurt Parliamentarians and National Identity. Cambridge, Mass: Harvard University Press, 2002.