Until the DMG comes out (and explains how diseases work), I'd suggest against using contagion (as a PC or monster). That gives plenty of time for an FAQ to clarify, or to find out that it's not an in-combat spell but more of a plot spell, because there are no combat effects until an incubation time (3 saves, or even an hour or whatever) elapses.
The spell description is not vague:
-- "On a hit you afflict the creature with a disease of your choice."
Each disease consists of an effect or list of effects. Being afflicted with it is equivalent to being subject to those effects.
-- "After succeeding on three of these saving throws, the creature recovers from the disease."
If the effects had not yet begun while the saving throws were being made, there would be nothing to recover from.
Keep in mind that this is a 5th-level spell, and it only affects a single creature. Three rounds of guaranteed debuff (not even damage!) is not so much to ask from a 5th level spell. Further, you must succeed on an attack roll, which means you're going to miss sometimes, particularly if the target has a high AC.
Yes, slimy doom is a potent effect, but it's not much worse than hold person, which is only 2nd level (and can scale up to target more foes, whereas contagion cannot). In fact, plenty of spells of 5th level and lower can immediately take an enemy out of the fight if they land: dominate person, telekinesis, wall of stone, banishment, polymorph ... the list goes on.