How to deal with my academic advisor who offered me a postdoc position and try to prevent me getting other offers?
This is a common reason why job references are normally asked from the former employers but not from the current employer. If the current employer would like to keep a specialist, adequate recommendations just cannot be provided because of the conflict of interest.

Try to get alternative recommendations. Maybe your work included cooperation with other laboratories, or maybe you had some more junior "intermediate" supervisor, or maybe you have worked along speciality at least part time? Suggest these people instead. 

In the worst case, you may even ask for recommendation from another co-worker like you. Not very good yet better than nothing.