With that sort of peep there is no good reason it should not line up when you draw. That is the whole point of using the tubing. So now you get all the bad parts of using the tubing and you don't get the one benefit it provides.

You may need to replace the tubing, it may be too long or your peep is installed incorrectly and is so far off the tubing cannot correct it. Has it always done this or is it a new thing?

I suggest going to your local shop and have them help you adjust it (unless you have a bow press). Take the tubing off then draw the bow and see where the peep ends up. And while you are doing this you might as well check to see that it is properly located.

Close your eyes and draw your bow to your normal anchor points. With your back straight and your head straight (don't bend into the string or cock your head) then open your eyes. The peep should be right in your line of sight. You should not have to move around to line up with it. If this is not the case take this opportunity to correct it. There is a chance the tension of the peep tubing pulled the peep up in the string. Or it may not have been installed correctly in the first place.

Once you get the peep in the correct location have the guy at the shop add or remove a half a turn or so until the peep rotates correctly when you draw it. Or as close as you can get it. Then if you still want to use the tubing get some new tubing and cut it just short enough to pull the peep into the correct position.

Using a string loop will help with peep alignment and you could ditch the tubing and big heavy peep sight.

Or you could learn to shoot without a peep sight if you are just hunting with the bow. I used a Timberline No Peep to help train me to shoot without a peep and have no problems suggesting one.

You will probably have to re adjust your sights after doing any of things as well, so take your first shots close to the target.

Good luck,
Paul