Once your opponent is on the ground, you must make full use of the Grapple Assist.
What happens is that once you have chosen a goal in Grapple Assist HUD using the LS key, Grapple Assist will select the best possible transition on its own to get you to your goal.
With Grapple Assist switched on, LSUP for your Closest Getup, LSLEFT for your closest Submission, and Left Stick RIGHT for your closest Ground and Pound Position.
To get to your best Ground and Pound Position or Highest Level Submission, hold LB.
In multiplayer, it’s best to use Hybrid or Legacy Grapple HUD to minimize your transitions’ predictability and give your opponent an unnecessary advantage.