Box 3 taxes value, not income
The Dutch approach is the thing to grasp first. Instead of taxing the interest, dividends or gains your Indian assets actually produce, the Netherlands puts savings and investments in Box 3 and taxes a deemed return on their total value, minus debts, above a tax-free allowance, at a flat rate. So it is closer to a wealth tax than an income tax. Your Indian bank deposits, listed shares and mutual funds all go into that Box 3 value.
This is where the NRE surprise comes from. In India, NRE interest is exempt, so people assume the money is tax-free. But Box 3 does not care about the interest; it taxes the deposit's value regardless. So a large NRE balance is taxed in the Netherlands every year even though India charges nothing on its interest. There is relief in one direction: after recent Dutch court rulings, you can now prove your actual return was lower than the deemed one and be taxed on the lower figure, which helps when a deposit earns less than the assumed rate.
The interest and dividends India still taxes
India continues to tax some of the same assets in its own way, and the two systems have to be reconciled. NRO interest is taxable in India, with TDS under Section 195 that the India-Netherlands treaty caps at 10% if you file a tax residency certificate and Form 10F, and Indian dividends are taxed at a treaty rate of 10% too. The Netherlands then gives a credit for that Indian tax against your Box 3 bill.
The catch is that the credit is imperfect. Because the Dutch tax is on a deemed return on value, not on the actual interest or dividend, the credit for the Indian 10% is capped at the Dutch tax attributable to those assets and may not fully absorb it. So do not assume the Indian withholding simply washes out; sometimes a little sticks. The practical work is to cap the Indian tax at the 10% treaty rate with the right paperwork, so at least nothing over the treaty rate is left stranded.
The upside on gains
Here is the genuinely good part, and it is often missed. Under the India-Netherlands treaty, a gain on Indian mutual-fund units, and on a small shareholding of under 10% in an Indian company, is taxable only in your country of residence, the Netherlands. So with the treaty claimed, India cannot tax those gains at all. And the Netherlands does not tax gains separately either, it only taxes the annual Box 3 value. The result is that gains on your Indian funds and small share holdings can end up bearing no capital-gains tax in either country, just the yearly Box 3 charge on their value.
That is a real advantage worth securing, and it depends on the details, that your shareholding is genuinely under 10%, and on the fund units being treated as units rather than shares. A practising CA confirms the treaty position, files to stop or reclaim any Indian tax on a gain the treaty assigns to the Netherlands, and caps the Indian tax on the interest and dividends, so you keep the advantage and lose nothing to over-deduction.