Hi Mike,
Some digital meters (amp or volt) can not use the same power supply because that puts one of their other connections connected to one side of the power supply, and if that has to connect to another meter using the same power supply it will cause a big problem, at the least the meter wont work.
There are meters out there that can measure the same voltage that they run off of, but im not sure that would work either because there is still the ground lead that is common to both power supply AND one input lead.
To be safe, you'd have to use two separate wall warts or whatever you can find, or else check to see if you can find any meters that dont have this requirement.
Note i did not read the spec's entirely, so i cant say for sure if these particular meters have this kind of problem, but most meters do have this problem so at least be careful.
There also may be one very careful way of wiring them together so that you can use one power supply, but you'd have to be sure that the meters can work that way. For example, if the volt meter used its negative terminal in common with the negative power supply, and the amp meter used its negative terminal in common with the negative supply too, then you might get away with using the same power supply for both if you connect the amp meter and volt meter negative terminals together.
The only caution here though is again, that many meters dont allow a common connection between their negative power supply and their negative input measurement terminal, so you'd have to check the specs out very carefully before trying this.
Let me ask you this, how did you find out the volt meter would blow up?
I noticed there is "ask a question" at the bottom of that page for the volt meter. Maybe you could ask the seller.
Many meters that do NOT have the power supply grounding problem actually state that in the ad writeup that says something like, "meter can measure its own power supply".
One test that might work is to use an ohm meter between the negative of the power supply screw and negative of the meter measurement screw, and see if they are connected together (or trace out the PC board). If not, then the meter needs its own separate isolated supply like a battery or separate wall wart.
Here is a small diagram to help explain the difference between meters and how they can be connected together.