Nginx PHP-FPM Timeouts
Unfortunately Nginx + PHP-FPM configurations do not respect PHP’s set_time_limit() function. There’s a couple of ways you can minimize the likelihood of a timeout.
You can try lowering the “Maximum Request Size” setting using the slider control on the settings tab of the Migrate DB Pro plugin page. The minimum size is 512 kB.
The other option is to have your web host increase the Nginx’s request timeout setting.