What happens when a file size limit is reached?
No, the two are unrelated. 

TempDB is used for explicit temp tables, but also for sorting and database snapshots and lots of other internal things. Was there some other very large transaction going on when the TempDB filled up?

If a transaction needs more data space (or log space, or TempDB space) but the file is set to not grow (or there is insufficient space on disk), the transaction will fail and roll back. So no new data will be added.