Once your WP and extension of stay based on business has been done, the cost for both the WP and extension fees are supposed to be paid by the company, correct?

Are their any written rules that state this?

My new company is trying to be funny by saying that just because the invoice on the respective reciepts has my name, it'll be deducted from my salary over a period of months.

Whats the best way to go about resolving this?

You don't need read any further than your contract. Those things are usually part of the agreement. The law don't care who pays what.