Assuming that the criteria by which the offer of asylum is offered is based on human values, how can it be offered without violating the prime directive?
The Prime Directive (also known as the most routinely violated capital law in history) forbids the interference in the overall development of a non-warp-capable culture. I think it's been defined differently in different series, but the first time we get a real description of it, in the original series, it is given as:
"No identification of self or mission. No interference with the social development of said planet. No references to space or the fact that there are other worlds or civilizations."
Note that the reference is to the social development of the planet. Actions which affect a single individual, which cannot subsequently impact the planet as a whole, would appear to be legal under the prime directive.
Furthermore, according to the Star Trek Technical Manual, there are exceptions:
But this principle shall not prejudice the application of enforcement measures under Chapter VII.
This would imply that there were recognized legal situations where the Prime Directive can legally be ignored in the cause of justice. Someone in need of asylum may fall into this exemption.