| Probably not.
It sounds to me like your NJ company is a company that provides temporary workers. If so, then their base is in New Jersey, and that makes you subject ONLY to NJ taxes.
The only way you would have to pay NY taxes is if your company agreed to provide you to a NY-based company under a intermediate-to-long-term basis (at minimum of 4 months). If that happened, then there would be some legal basis for requiring you to pay NY state income taxes.
For now, you are like any other business person who visits NY multiple times of the year. As long as it is not projected that you will stay in NY for an extended period of time, your situation is just fine as it is. | 
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