AC or DC current setting shouldn't matter.
What matters is the additional inductance (just the wires, the DMM shouldn't have too much inductance) that you place into the ICs power supply input by connecting the DMM.
A common thing with these small buck converter chips is that they don't have any headroom for input overvoltage - AFAIR this is a 20V abs max specified chip and so may blow up at maybe 22V.
By placing inductance into its power input, the switching causes more or less ringing, then you have your usual ceramic capacitor here which doesn't really dampen the ringing - this way you can generate enough voltage at the input to blow the chip.
This is my guess what happened, there's an app note by Linear Technology adressing this issue.
In short: If you want to measure the input current of such a converter, or have a somewhat longer input power wiring, always place an additional electrolytic capacitor in parallel to the ceramic one, this does a good job to dampen the ringing. Never insert the DMM between the capacitors and the ICs input.