Instagram does not allow instant publishing from 3rd party apps (yet!). So, unfortunately, whilst you can post instantly to Facebook and Twitter, it is a two-step process to publish to Instagram.
When you share to Instagram, you will get a notification asking if you want to Copy and Download - this refers to copying the caption, and downloading the image/video to your device.
Select Copy message and open Instagram; this will open up the Instagram app where you can select the image/video and share the post.
(Make sure you are logged into the right account, as instagram will open to whatever account is currently logged in on the app)
When it comes to writing the post in Instagram you can just press paste and it will transfer the share text you wrote in the Players' Post app (so you don't have to write it all out again).