Let me explain a little bit more....
the deobandi school of thought follows an extrem-ish vesion of hanfi school of thought. Ghair muqalids don't follow ANY school of thought, they combine all four and don't mind the minor differences. Saudis love this idea because that's how they think they can unite all muslims. zakir naik and peace tv etc, they're not deobandis, they're ghair-muqalids, they don't like to be called hanfis, sunnis, shia, anything except muslims. Deobandis and ghair-muqalids have their differences. Plus deobandis have differences with the saudis as well. Maybe deobandis get something every now and then and btw I also heard of that saudi royal visiting their "headquarters" in deoband. But the real funds go to the zakir naik movement. Everyone in the middle-east just love that guy. And I don't think they're funding any extremists or terrorists.
Let me repeat again Zakir Naik and deoband movements are not linked, they are two separate entities, they even have conflicts on many matters. Other than that, I do think that large funds come to peace tv and group from all over the world, not just saudia in particular. In my opinion, peace tv and group are clean.
The kind of terrorist madrassas your talking of are not funded through clean money, they are funded through intelligence agencies. That kind of a madrassah and movement can popup almost any where around the world and gets dismantled when it's no longer needed. Do you remember how saudi intelligence warned russia not to interfere in syria or else they'd destroy their winter olympics....That kind of thing.
I don't think the deobandi movement in india is a terrorist outfit either, they seem clean. How ever, they do obviously produce extremists. But there's a difference between an extremist and an extremist+terrorist.
And btw tablighi jamaat is not linked to ghair-muqalids or peace tv or zakir naik. Tablighi jamaat is an entirely different setup. It's a global thing. In Pakistan, they get around 3 million + in their ijtema. They have big support globally, operating "markaz"es in almost every country. Also, they send ulema and volunteers from all over the world to places where they don't have large followings. It is pretty much self funded. They go literally door to door, calling people to their jamaat. They are apolitical and peaceful. They're clean. They don't do politics, that's how they gained such a large following. They just tell you to be honest, pray, etc etc. That's how you will even see moderate shias in their gatherings sometimes. Even shias can follow them as they never get into the details of figh etc, they just focus on the common points.
So there you go, now you know the different religious movements that began in your very own India.