I think your concept needs to change.
PHP cannot schedule a job, neither can MySQL. Triggers in MySQL execute when a mysql query occurs, not at a specific time. Neither
This limitation usually isn't a problem in web development. The reason is because your PHP application should control all data going in and out. Usually, this means just the HTML that displays that data, or other formats to users, or other programs.
In your case you can think about it this way. The deadline is a set date. You can treat it as data, and save it to your database. When the deadline occurs is not important, it is that the data you have sent in your database is viewed correctly.
When a request is made to your application, check if the date of the deadline is in the past, if it is, then display that the project is closed - or update that the project is closed, just before display.
There really is no reason to update data independantly of your PHP application.
Usually, the only things you want to schedule are jobs that would affect your application in terms of load, or that need to be done only once, or where concurrency or time is an issue.
In your case none of those apply.
PS: I haven't tried PHPscheduler but I can guess it isn't a true scheduler. Cron is a deamon that sleeps until a given task is due in its queue, executes the task, then sleeps till the next one is due (at least thats what it does in the current algorithm). PHP cannot do that without the sockets and fork extensions, as special setup. So PHPscheduler is most likely just checking if a date for a task has expired, on each load of a webpage (whenever PHP executes a page). This is no different then you just checking if the date on the project has expired, without the overhead of PHPScheduler.