It shouldn't be the case, no. Delaware won't tax his income, because he is not living in Delaware. However, his income can be factored in to determine Delaware tax. Delaware would pretend that all of your income is taxable in Delaware, and then prorate the tax to the percentage of income earned in Delaware.
However, Delaware does give you the option to file as Married Filing Separately even though you are filing jointly on the Federal return. If you wish to explore this option to see if that would result in a lower Delaware tax calculation, please see this FAQ: https://ttlc.intuit.com/replies/3301995
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