You aren't being double-taxed, because of the way each of these states calculate the tax due from that state.
Tax for NY residents is computed using total income from all sources, but then you get a credit for taxes paid to the other states on the same dollar of income. You don't get taxed twice, but you do end up paying the highest tax rate among the states on that dollar.
The NJ nonresident return first calculates your total income from all sources, and then prorates that taxable income to NJ based on a ratio of gross income from NJ sources to gross income from all sources. So, on the summary screen for your NJ taxes, you should see the "proration" of NJ taxes, such that you only pay NJ taxes for the NJ portion of your income.
The CT nonresident return is similar to NJ, in that it appears that all income in included. But, CT uses a similar ratio to reduce the total income from all sources to the only the amount sourced in CT.
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