Picking has no effect on timelines, the only thing that is payed attention too are the tags. So if you have a bunch of timelines playing with the same tag, when you pause using that same tag all of them will be paused.
One way of uniquely identifying a timeline is to give them a unique tag, possibly based on the UID of the instance involved. Then when you want to pause a specific timeline, recreate the tag after picking the instance you are interested in.
Can you post your project or a sample of what you are doing so I can understand better what you are trying to do?