We use multiple tees to work on this. You can use two or even three.
With two tees, put one a little deeper into you than you normally think you like to make contact. Put the other ball maybe 3" directly in front of it on the same level. Then work on hitting both for line drives with one swing.
With three tees, put the middle ball where you like it, the other two balls 2" ahead and behind. Again, swing to get all three hit as line drives.
You can combine this with use of a tool like the Instructo Swing swing trainer for instant feedback without a coach's help.
What you're describing is a typical comment from a coach to a player whose follow through turns off too soon. These drills will help you build the habit of following through more on the path of the ball. This way if your timing isn't exactly perfect, you still can hit the ball reasonably well. Think of the middle ball as a HR if you get it there in a game. The other two balls may not go out but can still be decent hits.