Wow, that's pretty brutal. I can't look at my PHB right now -- were there any changes from the alpha (if you have access to both)?
I think it was intended to take effect right away and not be cured for at least three rounds, as written. The problem for legendary monsters is that they can't avoid the whole thing up front since the initial effect is based on an attack roll rather than a save.
If it hasn't changed from the alpha, that's the strongest debuff I've seen in the game so far, and as a 4th-level Cleric/Druid spell.
It is a level 5 spell now. I don't have access to the alpha at the moment.
To be clear, my belief that the intent is for the target to need to fail three saves before being affected is based on balance considerations and not the verbiage of the spell. As written, it seems clear that it takes effect right away.
But, compare it to Hold Monster, another level 5 single target debuff. HM is a concentration spell, it allows extra saves every round to shake off, and it allows a save right at the beginning to resist it entirely. Contagion does not require concentration, lands with a melee spell attack, and then evenlegendary monsters are affected for a minimum of three rounds. Have one ally and choose Slimy Doom and you have stunlocked the enemy for three rounds. If it survives those three rounds by some miracle, do it again.
That's why I think the intent is for the monster to need to fail three saves before it takes effect. Otherwise, it is just way better than other spells of similar level. Heck, is is pretty competitive with Power Word Stun, an 8th level spell.
Dragon slayer spells, indeed.