PHP evaluated in rule works locally but not on remote server
Please follow below steps to debug.


Enable Rules Debug settings.
Enable the rule you created.
Check the messages given by rules debug messages on rule activation conditions.


Still if you cannot able to find the solution, check the error logs. 

You may need to change the format of collecting node values. Using "und" $node->field_project_skills['und']['0']['tid'] is not the right way. You can check below post that explains right way of reading node values.

http://www.computerminds.co.uk/articles/rendering-drupal-7-fields-right-way