There is not that much difference to tempdb in Azure that it is on-prem. In both cases tempdb can grow until it hits some limit. On-prem that would be the amount of free space on the disk. Or any max size the DBA has configured for tile files. I would guess that the latter applies in Azure, and the exact size depends on what service level you have.
Tempdb can grow because of many things:
- Temp tables and table variables.
- Sort and hash spills.
- Spool operators (i.e. worktables).
- Version store.
I may have forgotten some.
If one particular SP fills up tempdb, I would assume that there is a query in that procedure that produces any of the two in the middle.