Are you an EU national? I'm not really sure who handles the visa applications for an employee. I think it depends per company. I've worked in a couple of multinational companies in Manila and they are the ones who handle the process for visa applications for their employees from overseas that are on-shore in Manila. They are the sponsor, so they handle it themselves. Although there are some that would let you do all the processing and then they'd reimburse all the cost. There is no standard in the Philippines when it comes to this as far as I know.
With regards to when you need to apply, it's a requirement that you have an employee contract when you apply for the visa. That means you already acquired the job. If you don't have a sure job yet, then you won't be able to apply. The only thing you can apply for is tourist visa.
Have a read on these links I just searched.
http://immigration.gov.ph/visa-requi...mployment-visa
https://emerhub.com/philippines/appl...e-philippines/