When a process is already in progress, the trainer does not always complete that process. The trainer does complete once that process is completed and a new one starts. So, it isn't that the trainer doesn't work, it is more like the game locks in the countdown and will not complete genome extract, dig sites, research or incubation until the first one is completed.
In my game, with 6 queued genome extractions, the first is unaffected by the trainer but the rest will complete immediately with the trainer. The same is true for incubation, research, and dig sites in my game.