In my opinion, if the company wants you to have a specific logo on your shirt or jacket then it's up to the company to supply it for you.
You don't mind paying for the standard pilot's shirt as you can take it to the next job easy enough.
However, the award does state that if the company requires a uniform to be worn on duty then an amount of $250 will be paid to the pilot on commencment of employment (and annually thereafter), I am sure that this would go a long way towards paying for those logo specific shirts that are required.
This applies if your casual, part-time or full-time.
Cheers,
Capt EFIS.