Has all to do with your bank and nothing to do with the DR
Ask your bank, all differ in terms of Plus/Cirrus access. It sounds unusual that a particular type of account has no fee vs. one than does since the interest paid on savings nowadays is essentially zero so they aren't making it up that way. In your case at least you know that the savings account is a preferable source of the cash.
If the machine IN the DR charges a fee at the time it will be on the receipt or advised in advance, e.g. in the US and Canada the ATM often says it will add $1.50 for itself if it is not your own bank. But your bank's fee it charges you is not DR related.
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