Ensure that your pointing at the same system-under-test when running locally and try again. Sometimes a test will pass locally because when running locally it's pointed at a web server on local host or a development environment, and then when running remotely it's pointed at a QA environment. Environment differences can cause test failures (and even be bugs)!
Make sure your timeouts are set appropriately. All tests that interreact with websites have timeouts (even Cypress). When Testery runs a test, you are getting a clean test runner that doesn't have the same items in its browser cache, the same network latency, or likely the same CPU and memory profile as your beefed up developer workstation. Whilee test run times are generally significantly better than running locally, this is due to parallelization, as individual tests can take longer to run.