Right, this is really working on my nerves, but Instagram has to do something about their bloody documentation.
I am already trying for a week to live update my website
When you get a subscription push, you need to query that endpoint (tag / recent).
I normally start an synchronous thread to perform this so I can answer in under 2 seconds to Instagram.
Then you parse that endpoint and look for a "next url" value.
Keep querying that end point, parsing the media and going to the next url until you find your stop condition.
For me I try to match 10 consecutive records in my DB. Basically from the tag, I store media when then meet my business rules.