For primarily work purposes???

Please look at this sentence.

"Employees given a cell phone for primarily work purposes will no longer be taxed"

I think this sentence is wrong in grammar. Because "primarily" is an adverb. Its location has to be before "for".
I mean, like this.

"Employees given a cell phone primarily for work purpose will no longer be taxed".

Could you tell me your opinion? If there is something wrong in my thought, please correct my view.

Thank you for your answer in advance.