As someone who outsources a lot and I believe I do so relatively successfully, there are a few issues here.
If this designer copied and pasted an existing design, swapped the header and said it took 5 hours, then thats an outright scam in any country, it doesnt mean third world labor is more likely to scam you, it can really happen in any country.
Having said that, you do have to treat overseas labor different than you would a westerner.
A good example is if you want a door installed over there. A westerner would install the door, have 2 hinges on the side and a handle. Its assumed that when you say "Door" you also want the hinges and the handle.
I have found in personal experience, mainly with Indian contractors, that you have to be super specific about what you want. I want a door, of this size, over there, with 2 hinges, opening in this direction, with a handle located there.
I think it may be a cultural thing or perhaps since they are working for so little they do the absolute minimum, Im not sure.
With overseas labor you have to control the project very tightly. Here are my tips:
See a portfolio of their work first, check out the code, see if its original. If its a outsourcing job site, check out their feedback.
If its a larger project, give them a small test task that requires the skill that the big project needs that will take no more than an hour. Observe their skill/speed/responsiveness/quality. If they are crap, you are only out a few bucks rather than finding out months into a big project. I have found that many overseas contractors on the outsourcing sites will snap up any work they can without actually having the time or skill to pull it off. The test tasks filter out these people.
In the project brief, be stupidly specific (as in our door example) and be sure to add in lines like "All work needs to be original". While you would assume that all work would be original anyway, others dont seem to think that way. Thats why you have to really spell out the terms.
With the payment terms, work something out that limits the financial damage if they are bad. Ideally pay after you see work. If you have to pay something up front, try and keep it to a smaller percentage.
If its a large project, require daily/weekly updates about the work that is being done (depending on whether they are solely working on your project or not). I dont bother with this on small projects, but on big ones I do. Set up milestones on when things must be complete.
Managing like this is the cost of cheap overseas labor, if you can do it well its great. If you find a great overseas contractor that has proven to be reliable in your past projects, then you can obviously loosen the reigns. If you dont want to do all this then stick to a westerner instead, but you will pay for it.