If the high seas fleet is fully intact and the other allied powers have made peace with Germany, it is possible that the Germans would threaten to send their fleet to reclaim their territory, though this would likely be something of a bluff. If Germany receives its other colonies back, Japan would possibly agree to withdraw under such pressure.
If Germany's victory is more tenuous, it might not receive its colonies back from France and Britain. With its empire gone, Germany would probably offer to sell its the Caroline islands and the Marshall to Japan as Spain had done 20 years earlier.
Whatever happens, it is very unlikely that German-Japanese relations will be friendly for quite some time. Firstly, the Germans were acutely aware of Japan's alliance with Britain and resentful of its opportunistic declaration of war against their nation and decently, Kaiser Wilhelm, for not fully clear reasons, intensely dislike the Japanese. These two factors alone would create enmity enough but an unfavorable settlement for Germany regarding Tsingtao and/or the Pacific islands would all but guarantee German opposition to Japan for at least a decade and probably quite a bit longer. If any mending of relations occurred, it would be by Japan which would see Germany as a potential ally because it lacked much territory in the East and thus Japan would never have reason to go to war with it again in contrast with Britain, France the Netherlands, Russia, and especially the United States (which the Kaiser and some others feared).
Regardless of what Japan wants, I strongly doubt that Germany would support it if it tried to pull stunts like it did OTL in Manchuria and China and I think the Germans would ultimately ignore the Japanese for the most part not daring to risk allying with them as that would provide no real benefit nor would the Japanese have many resources or goods to offer them (unlike China).