who pays for H1B Transfer premium processing cost, employee or employer?

[Jacobdeiter]

I am on visa and planning to transfer visa to new IT consulting company. The consultancy recruiter says that they will take care of the cost for transferring my visa but if it is filled in premium mode then I have to pay for it. Is it a regular one, can I trust the consultancy?
when I check the consultant reviews in internet it says the company has more than 1000 employees.