What's the default way to interpret the phrase "Don't waste any time (in) getting back here."?
Solution 1:
I suppose this could, technically, be ambiguous. However, colloquially, it's quite clear the sentence refers to your second interpretation. "Don't waste any time doing x" is a common phrase to suggest that they need to do x and only x in a timely manner.
If they were saying they shouldn't come, they'd use "Don't waste your time" or "Don't waste my time" (if they wanted to particularly point out their annoyance), rather than "Don't waste any time".