Mango, the bottom tug should be snug, yes, but not tight.
Pardon me while I run off on a bit of an educational tangent
The idea behind breast collars is to keep the saddle from sliding back either during extreme riding situations like high speed or steep hills, or for when you are roping and you need to drag something. Ideally, if you were to pull on the center D-ring of the breast collar, all 3 tugs should come tight at the exact same time and the center ring should not change its relative position on the horse. It should pull straight out from the chest without moving up, down, or to either side. If it doesn’t change position, then that means that the collar is adjusted correctly.
If the bottom tug is left long, like so many people do, and the saddle is suddenly pulled back, then the top 2 tugs will come tight long before the bottom one does. When that happens, not only does the BC pull back, but it pulls upwards. If it is allowed to pull tight over the place where the horse’s neck meets their chest, then the horse will choke down after only a short length of time. I’ve seen that happen dozens of times, mostly when roping, but it wouldn’t surprise me if it happened on a steep incline either. Not only is that a risk, but a hanging BC tug is no different than a hanging back cinch. When you are riding trails, anything hanging 3 or 4 inches off the horse is a perfect place for a tree branch to get hung and tear up both a good horse and some good tack.
I like to have no more than 2 inches of hanging space between the bottom tug of my BCs and the chest of the horse. That is snug enough to be effective but loose enough to be comfortable. I thoroughly hate the traditional types of breast collars because none of my saddles have the specially designed D-rings up closer to the swells. Trying to fit a BC with it attached to the cinch D-rings was absolute hell to keep it loose enough to not rub sores and tight enough to keep it in place. That’s why I only use the pulling type collars.
When I adjust my BCs, I like to center that center ring a little bit lower on their chest so that there is zero risk of cutting off their oxygen, even on horses whose necks tie in low. After I get the bottom tug adjusted where it is just right, I simply buckle the upper tugs where they keep the center ring centered on the chest. Just to share a few pictures of how I keep mine adjusted so that you can kinda see what I’m talking about….
The bottom tug on this guy was a bit looser than I like, but he was so small that my BC simply didn't have enough room to go any tighter than this.
Even this little narrow guy. It was centered a bit higher on his chest than I like, but he was one of those horses that the entire thing was almost too big for LOL.