What exactly does the Vim shortcut run when executed? fwiw, tests should reside in MyModule/t/*.t. Also, you never specified which directory you are in when running the test command. You should be in the distribution's root dir.
You don't need to make install to run tests. make test is a common way to run your suite (all tests), and it automatically knows where to look for your libraries. You only need to do things differently when running individual test files. make install works, but as haukex stated in an earlier reply, it isn't necessary. Both of the below will work all the same, without installing (granted you're in the dist's root dir as I've said):
"perl -Ilib t/foo.t should be enough. Update: or prove -l t/foo.t."