There are large number of surname variants based on the German nickname "Till" (short for Dietrich, and similar names) -- T*L + various suffixes -- that are found in all German-speaking areas.
Thillman is included under Thiel and its variants in Bahlow's Schlesisches Namenbuch.
If you read German, "Schlesisches Namenbuch" has a summary of surname development in Silesia in the Introduction (Einleitung: Die schlesische Namenlandschaft).
With a mixed ethnic population going back centuries (there are tribes listed in ancient texts whose ethnicity is still disputed), surname development in the 14th and 15th centuries incorporated elements of many languages. Once surnames were regularly passed down in the father's line, the descendants (regardless of that one ancestor's own ancestry) might identify with whichever heritage was the most significant to them.