The threshold of temp table in stored procedure is little bit tricky, it doesn’t exactly follow the regular threshold.
First of all, you can’t use the modification_counter to determine when auto update statistics happens. Because the data in tempdb is deleted every time after execution, replying on the data that that already deleted does not any sense.
Secondly, the algorithm is different:
Here is the original threshold of temp table that are not in stored procedure.
Here is the new algorithm. (note, compatibility of user database decides old threshold or sublinear threshold, the compatibility of tempdb does not