First of all, welcome to the community.
If I understand your problem:
You wrote a PHP application that uses Transmission Api to connect to it In order to implement various functionalities add torrent, delete it etc.
Your problem is that when multiple clients connect to the application to start downloading a torrent file, only one of them, could do it.

I would say that if you have posted your question on Stackoverflow or similar question/answer sites or forums specialized in programming
you would get responses faster than in here. Because, after all, not everyone in here is a developer so high chances no one will answer.
As an aside, don't forget to post a snippet from your code when asking such questions because your problem can be in different portions of code.
Goodluck!