The fear is reasonable. Most people have seen cheap work, and they assume a lower price always leaves a mark somewhere in the output. So the burden is on us to prove it does not.
We hold one bar regardless of market. The same review process, the same senior sign-off, the same refusal to ship filler. Where the work is made changes the invoice, never the craft that leaves the studio.
What the cost advantage does change is how much of your budget reaches the actual work, the media, the engineering, the creative, instead of overhead. That is the part clients feel, and it is the only part that should.