Yes, the goal is to have all shots leave during the upswing of the cycle. I'll steal a few of Varmint Al's diagrams that illustrate this. The first one is of a 24.75" reverse taper barrel without a tuner installed, typical of winning barrels that used to be pretty common in the benchrest world for a number of years not all that long ago. In the left image you can see that without a tuner on it the barrel is kind of straddling a peak node with these shots. The red dotted vertical line represents the exit time of a 1035 fps shot, and the blue dotted line is that of a 1075 fps shot. Then in the right image the curved line from left to right represents the muzzle projection at the target, red for the slow shot and blue for the fast shot. That is, anywhere along that line if the bullet exited at that time it would hit the target with that elevation. It is where the barrel is currently aimed, all along that curved line at that point in time. And where the dotted lines cross the curved line is where the shots actually left, so they hit the target at the elevation where each line meets its dotted line.

Straddling the peak node like that isn't ideal. This seems to result in a vertical delta between the shots of about 0.0764" or so, with the slow shot hitting higher. Kind of hard to measure with how low resolution the images are. Now we look at the same graphs with a 4.9-ounce weight installed at the muzzle.

You can see in this left image this has slowed the overall movement of the barrel down, and has moved both shot exits away from the peak node and now they're both exiting during the accelerating upswing. As a result, the right image shows their vertical delta is now fairly small in comparison to what it was without the weight installed. The delta now seems to be something like 0.0291" here. A nice improvement, but the slow shot is still hitting slightly higher, so we'd still like to slow the barrel down even more that the 4.9-ounce weight did here. The next one shows the same graphs, only this time with 8.6 ounces of weight installed at the muzzle.

The muzzle movement curve has an even gentler slope now, so it has been slowed down even more than with the last weight. Now the vertical delta between the two shots has shrunk to something like 0.0073" and seems fairly close to ideal now. We're very close to no difference at all. The next example jumps from 8.6 ounces of weight all the way to 16 ounces. A whole pound of weight added to the muzzle.

Now it has slowed it down a whole lot more, and the upwards swing doesn't really seem to be accelerating anymore. It hasn't quite reversed direction, but it has slowed enough that now the slow shot is hitting noticeably lower than the fast shot. It seems to be about 0.02" lower now compared to the fast shot. So 16 ounces would seem to be a lot more weight than you'd like on this barrel. The ideal would likely be pretty close to the previous 8.6-ounce weight. And so, ideally, your tuner would be close to that weight, just a hair under what might actually be ideal, and then you move the adjuster to dial it in just-so.
edit: And if shots actually leave with the barrel in a downswing then that means the fast shots are aimed higher than the slow shots. And since slow shots are already going to fall more by the time they reach the target you don't also want them to be aimed lower. This will do nothing but give you a huge vertical delta. Shots leaving during an upswing means the slow shots leave at a steeper angle and that compensates for their greater drop due to the lower velocity, reducing the vertical differences. Downswings make the vertical differences even worse.