As MySQL documentation on information_schema.tables says (emphasis added):
Beginning with MySQL 5.7.2, UPDATE_TIME displays a timestamp value for the last UPDATE, INSERT, or DELETE performed on InnoDB tables that are not partitioned. Previously, UPDATE_TIME displayed a NULL value for InnoDB tables. For MVCC, the timestamp value reflects the COMMIT time, which is considered the last update time. Timestamps are not persisted when the server is restarted or when the table is evicted from the InnoDB data dictionary cache.
The UPDATE_TIME column also shows this information for partitioned
InnoDB tables in MySQL 5.7.8 and later. Previously this column was
always NULL for such tables. (Bug #17299181, Bug #69990)
Probably you are using innodb tables and your MySQL version is earlier than described in the documentation.