MBP has it in one ;)
If you are tipping forward, your core muscles are lacking.
Your core is the most vital part of your body when riding, as a dressage rider, I can proudly say that I have some ripper core muscles! You should be able to stop your horse through simply a firm engagement of the core.
To feel your core engaging, (this is a little X rated but it works!) imagine that you have a straw in your 'girl bits'. Now there is some tea in a cup at the bottom of that straw and you need to suck it up. Do it now, while you're sitting in front of the computer. Close your eyes and 'suck tea'. You'll feel your deep abdominal muscles contracting, not your abs, but your core, your deep internal muscles that keep your body upright! It's almost as thought you are 'lifting' your girl bits up without actually moving your pelvis or vaginal muscles. It all comes from the core ;)
Sorry kids, I know it's a bit of a gross analogy but its worked with everyone I've tried it on and was the analogy that finally clued me in on how to engage my core!
So now, back to transitions. Core core and more core is what is going to give you a beautiful, uphill, light, engaged transitions - I promise. If you just pull on the reins, hope for the best and get tipped over the dash in the process, the only place that the energy from movement can go, is onto the horses front legs, thus throwing it onto the forehand. It cannot possibly stay on its haunches if you just pull on the reins, unless you have some kind of freak of nature, Totalis type of horse, and even then, it will still tend to transfer more weight to the forehand despite being built so uphill.
Start working on your transitions by working on walk - halts.
I want you to get a nice, steady, even tempo walk going. Take a deep breath in through your mouth, and exhale slowly through your nose. Allow your body to relax. Now picture a slab of meat over a rolling pin. Now FEEL a slab of meat over a rolling pin. You are the meat, the horse is the rolling pin. Allow your legs to drape over the horses sides, relax, allowing your weight to sink into your heels and into your seat bones. Now 'suck tea' with your core.
If you get no response from your horse (and you may not - he's not used to responding to seat aids, and you're not yet proficient at giving seat aids) you may need to use SOME rein. The best way to use rein to stop, it to allow your hands to come level with the horse's wither, and come wide. This is the position in which you can easily access and engage your core while not relying on your hands to just pull back.
So you've dropped and widened your hands, now close your hand just a little, to put a slight increase of pressure on his mouth. Release, give, release, give until you get a reaction (aka downward transition - even if it's not to halt, just a slowing of the gait is good enough for now!).
The goal is to be able to simply drop your weight down your legs, engage your core and the horse will stop. After all, if he can feel a tiny fly landing on his body, he can sure as hell feel a difference in your seat!!!