There's no reason to expect any systematic difference. The store-brand ones and the brand-name ones might well be the same cashews in different packaging. And the FDA (and other agencies) are perfectly content to let everyone put the same nutrition facts on their cashews without any sort of individual testing, whether or not there may be underlying variability.
For what it's worth, the FDA does report nutritional information based on two trials for cashews (not exactly high confidence) and the minerals you're interested in don't vary much between the two: copper by 7%, zinc 5%, phosphorous 10%, manganese 1%, and magnesium 2%. That's all just relative percentages between the two trials - converted to daily values, copper varies by 2%DV, zinc 1%, phosphorous 2%, manganese 0.2%, and magnesium 0.2%. (Note that some things do appear to vary more, e.g. sodium changed 50%... but it's still only a 0.2% daily value change.)
So I'm sure it's possible for cashews grown in different places to have slightly different mineral content and so on, but there's no way to tell by the time it's all packaged to sell to you.
So in the end, based on that admittedly low-confidence data, the variation isn't that much to begin with, and you don't have any way to find out anyway, so might as well not worry about it. There are better ways to make sure you're getting enough of a given mineral.