Do you only need to use a timestamp when citing direct quotations from movies? Otherwise, could you just do in-text citations as (Producer &
When thinking about when to use a timestamp, it's similar to deciding when to use page numbers when citing a written document. Certainly the timestamp is required for a direct quotation, but it can also be used when paraphrasing if you think it might be helpful to the reader. It is up to your discretion. So if you are discussing a particular scene or statement, you might use the timestamp. But if you are discussing more general aspects of the film, you might not. The APA Style Blog has some additional insights on this question.
When doing the in-text citation, the producer(s) and director are treated like authors. So, you would use the rules for citing a work with multiple authors. If you have two producers and one director, that would be like having three authors. When doing this citation, you would list all the names the first time around, e.g. (Smith, Jones, & Brown, 2004), and then in subsequent citations of the work you list just the first contributor followed by et al (Smith et al., 2004). This helps to save space. Additional citation examples for multiple authors can be found here. Also, you don't need to indicate the producer and director roles in the in-text citation; that is done in the full reference in your reference list.
I hope this is helpful, and please let us know if you have any further questions on these or other citations.