That depends on what you had set up in files options (Main Camera Settings > Customize File Name). If it includes date and time, then it should not overwrite.
However, if the new file name is the same as the old file name, then the old file would be overwritten.
Systems like macOS prevents a user from overwritting by appending a " _ 1" (or " _ 2" etc) to a file name. ASIAIR does not do that.
An easy way to prevent overwriting is to edit the Target name before an AutoRun session. For example, change it from "M8" to "M8a". ASIAIR will create a different folder for the latter.