Is it possible to get tweets from specific users when they are posted?

Question

API

I can get tweets from certain users via the REST API, put them on cron, but sooner or later I will run into restrictions, and this method is not suitable - I receive tweets with a delay, because there are a lot of users (more than 1500).
Twitter has a streaming api, but I couldn't figure out if I can get the tweets of certain users until they are authorized in my application?
Actually, the question itself is how to get the tweets of specific users when they are posted?
If there is code - preferably php