I do not know how the companies that you've mentioned works.

However, can share with you how general recruitment agency operates.

1. Upon getting the job, you will be an employee of the hiring company.

The recruitment agency will get the first month of your pay. This is the preferred as you are a company staff and will get the related company benefits.

1. Upon getting the job, you will be an employee of the recruitment agency.

You will be seconded to the hiring company. The company will pay your recruitment agency monthly (eg $2000) and you get your pay (eg $1800) from the recruitment agency. Your recruitment agency will provide you will all the "company benefits" normally not as good as the hiring company.

Have friends (a few years back) got their job these way, that's why I know.

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Only the recruitment agency can confirm how they operates, each company is different.

Most importantly, read and clarify BEFORE you sign anything.