There is no delay from Broadcastify or the feed provider. There is a delay from encoding/decoding the transmission and sending it through the internet to you. This can take anywhere from 30 seconds to 2 minutes. If the feed provider listed what is being streamed then that is what should be streaming but it is not always 100% the case.
If the stream is busy or very busy, it is possible and likely you will miss transmissions. It is the nature of the beast in scanning. While one precinct is talking and the scanner is locked in on that frequency, there could be another precinct talking at the same time. You will miss that radio traffic. Since you are a premium subscriber, check out the Broadcastify Calls platform. See if someone is streaming that agency. The way it works, no radio traffic is missed depending on what the provider is streaming.
Trunked is the type of radio system, so go to that, then look for whatever dispatch covers the precinct. (They may have their own, or be paired with others.)I'm trying the check out that calls platform that you're talking about but I can't figure it out it's kind of complicated. For example I’m trying to monitor Minneapolis man 4th precinct. When I go to the calls platform it brings up something called Trunked.