MySQL Timestamp and NOT NULL

The reason is the different versions installed in the two environments.

The option for DEFAULT CURRENT_TIMESTAMP for datetime columns was added in 5.6 version (specifically in 5.6.5). See the doumentation about the DATE, DATETIME, and TIMESTAMP Types:

The TIMESTAMP and (as of MySQL 5.6.5) DATETIME data types offer automatic initialization and updating to the current date and time. For more information, see Section 11.3.5, “Automatic Initialization and Updating for TIMESTAMP and DATETIME”.

Most probably your Linux installation has an older version while the Windows has a newer. The solution would be to upgrade to the newer version (or have it installed besides the old).

General info about upgrading from 5.5 to 5.6 here: Upgrading from MySQL 5.5 to 5.6 and specific about upgrading in Ubuntu 14.04 LTS.

Don't forget to backup your data before you upgrade and run mysql_upgrade immediately after.

It actually doesn't accept NULL values it considers it as empty string. That's because you have your server in non-strict mode. That controls how MySQL handles invalid or missing values in inserts and updates. You can read more about modes here: http://dev.mysql.com/doc/refman/5.6/en/sql-mode.html#sql-mode-strict

mysql> insert into cities(state_id) values (20);
Query OK, 1 row affected, 1 warning (0.07 sec)

mysql> show warnings;
+---------+------+-------------------------------------------+
| Level   | Code | Message                                   |
+---------+------+-------------------------------------------+
| Warning | 1364 | Field 'name' doesn't have a default value |
+---------+------+-------------------------------------------+

mysql> select name is null from cities where id = LAST_INSERT_ID();
+--------------+
| name is null |
+--------------+
|            0 |
+--------------+
1 row in set (0.00 sec)

mysql> SET sql_mode = 'STRICT_ALL_TABLES';
Query OK, 0 rows affected (0.00 sec)

mysql> insert into cities(state_id) values (20);
ERROR 1364 (HY000): Field 'name' doesn't have a default value