This is exactly what I expect to happen on cards carrying a balance transfer; although, anecdotally some lenders don't do this. There are different ways lenders may approach this type of situation and from what I understand a lot of lenders nowadays do take the "pay all new charges in full PLUS your minimum and you're good" approach, but as I understand it the way Discover is doing it with your friend used to be standard, so it certainly doesn't seem even the least bit unusual or dodgy to me.
As DeeBee says, it simply comes down to which balances the lender applies the payments to.
My rule of thumb would be if I use a card for a balance transfer to make sure not to use it again under any circumstances until the balance transfer is 100% paid off. I'd also personally only do a balance transfer onto a card with a $0 balance, because I'd expect any pre-existing balance to be difficult to pay off once the BT hits - and it would thus accrue interest every month.
My advice would be to have your friend call Discover and ask them what, if anything (short of paying off the full BT) she can do to get the $30 charge paid off and prevent anymore interest.
