This is just like how the communicators seem to be psychic (like when say Picard hails Riker and Riker hears it as Picard is saying it). It's just a reality of doing a TV show...
Oh dear...
A "fringe fan" is speaking!
For those not aware, the tech specs written up for the 24th century combadges established that they work by way of subspace, and the computer monitors the channels. It hears who the person is calling, and immediately, faster than you can blink, sends the signal thru to the person the message is meant for.
I was just in our local wholesale club store this afternoon, and heard a very primitive example of the same sort of thing. (Something I've seen in other stores in the past.)
One of the workers picks up a microphone and pages someone. They put the mic. down. A moment later their voice goes out over the store's intercom, and you hear a repeat of what you just heard close up.
Why the delay? I dunno. Odd. Like the PA system recorded it and replayed it or something.
Well, in 24th century Trek, it works that exact same way, only it's channeled thru the computer and its subspace processors. It's virtually instantaneous. The person on the receiving end hears the call at almost the same instant the sender spoke. Then, once the receiver replies, the communication IS live.