The wrong-coloured rook pawn only draws if the defending king actually reaches the corner. With the king cut off, the attacker wins by shouldering it away while the pawn runs.
The previous drill can lull you into thinking that a wrong-coloured bishop plus a rook pawn is always a draw. It is not. The fortress exists only when the defending king gets to the corner (or at least to the squares g8/h8 before the pawn arrives). Here the black king is on c7, and White's king on f6 stands between it and the h8 corner.