This is a rather general question that can only be answered generally, and I think you may receive a better answer (especially to the latter part of your question) if you specify exactly which Greek "cults" you are referring to. No size fits all in traditional Greek and Roman religion.

You're correct-- in academic circles, "cult" (when referring to an ancient religious group) does not carry the same connotations as a modern cult. It does not imply that they only worshipped a single god, nor does it suggest hostile relations with other religious groups or any sort of fanatical tendency by modern standards. It is a bit difficult to pin down (or source) since it's just semantics, but in my own studies, "cult" refers more to its outlying position (as it appears to us historians, anyway) as a group than its inherent nature. But that's not to say that a cult is entirely separate from the most common religious traditions either-- it could be a special veneration of a certain deity that also appears elsewhere.

But the connotations of "cult" versus "sect" differ even in modern uses of the words. I'm assuming you're an American as "cult" is negative for you, but the term doesn't universally conjure images of Jonestown. I'm an American who did my master's in Europe, where "sect" is the term with the most negative implications, while "cult" is rather neutral. So from our perspective, the meanings are flip-flopped across the pond.

This is a pretty scattered explanation, but basically it comes down to the constructs historians use to understand what they study. It does not imply any specific nature or behavior as a group-- just that it is a group in its own right.