No, that's not correct. Massachusetts does not do that, nor does any other state so far as I know. If it did, then it would effectively be subsidizing the treasury of states with a higher tax rate, and of course states are not going to want to subsidize other states. As Massachusetts properly describes it, the credit for the tax paid to other states “is the smaller of:
• Massachusetts income tax on income you reported to the other jurisdiction, or
• The actual tax you paid to the other jurisdiction.”
You’ll find that stated here: https://www.mass.gov/service-details/learn-about-the-income-tax-paid-to-another-jurisdiction-credit
What this means is that the tax you pay on the income from another state ends up being taxed only once, either at the rate your home state imposes or the rate of the other state, whichever ends up being higher. For example, if the Mass rate were 5.15% and the RI rate was 5.99% then Mass gives you a credit against its tax for the RI tax you paid up to the 5.15% Mass rate; as that does not fully offset the RI tax, you still end up paying the extra 0.84% to RI for which Mass does not credit you. In short, you end up paying the 5.99% on that income that RI imposed. By the way, the federal foreign tax credit works the same way, too.