I'm not sure I understand the setup completely. When I asked about devices I meant everything. You didn't mention a display…which is essential for watching a movie. Also, you didn't mention how you're actually hearing the movies…Bluetooth speaker…display speakers…USB audio?
The MacMini has a speaker. When audio is through the speaker is there a delay?
It also has a 3.5mm headphone out. When you connect headphones and listen through those is there a delay?