Perhaps we shuld be more careful - there are, after all, three distinct questions here:
1. does superpostion imply many worlds?
Certainly quantum superposition and interference effects are part of the motivation of the Many Worlds interpretation of QM - so the one can be said to imply the other ... however, see 3 below, Many-Worlds is not the only interpretation as any reading of course materials will quickly show.
2. The fact that objects exist in superpostion which means they exist in multiple positions (proven fact), doesn't this automatically imply many worlds?
It is not clear what is meant by "objects ... exist in multiple positions" - does this mean at the same time? Perhaps an example of what is meant would be useful here?
The superposition in question is of position wave-functions - these are distributions of probability amplitudes related to the probability that a particle is in a number of positions rather than the actual position of the particle.
3. ignoring collapse interpretations, can there be any single world interpretations of quantum superpostion?
Well ... if we ignore alternative interpretations, we are left with Many Worlds - yes. I don't think this is what was intended though.
I think there is a basic misunderstanding here which StevieTNZ has touch upon: the math is not the object. When we say "a particle is in state Y" we mean that the things we are interested in about it are described by state-vector Y.
Any state vector can be described as a superposition of other vectors.
We choose the particular representation to suit the math we want to do - we could choose a representation in which the particle is in a pure state rather than a superposition. In which case, the same argument implies a "single world" event.
