As I understand it, Cardinal Burke was (or is about to be) ousted because he has made a habit of defiantly “correcting” the Pope’s more liberal statements in extremely public venues, strongly implying that Pope Francis is leading the church in the wrong direction, vindictively attacking other bishops he disagrees with, feeding conservative panic, and being generally abrasive. He is defiantly conservative in a church that is now trying to regain traction in the real world by including liberals as well as conservatives.
By and large, Pope Francis does decide on such demotions himself, and has demoted and promoted several clerical and non-clerical officials, sending very clear signals about resisting the tides of necessary change.
*Edit: However, I wouldn’t be surprised if he ended up with an unexpected post–Malta may be where he ends up, but nothing is official yet. Didn’t Pope Francis surprise everyone by promoting someone everyone expected he would demote?