From my understanding, when your pieces are on these entry squares, they are not moved into the 4 winning spaces. The game designer did however states that the active player (red) cant move the entry piece out of the entry sqaures onto the white spaces anymore, nor can the opponent (yellow) move into these spaces to displace the pieces back to their homelines.
I think these technical specifications disallow the red pieces on the entry spaces to sit in position to capitalise any opportunities to 'hop' outside onto the yellow pieces since the red entry spaces are so near the yellow homeline; ie. this will enable the first player (red for eg) who move his piece into the his entry square to have a significant control over his opponents pieces at the homeline while he continues to move his other pieces.
I also believe the piece can stay there if the controlling decide not to move it into either of the winning spaces, but i dun think there is a strategy in delaying entry unless the next move is sacrificed to urgently 'hop' an opponent piece etc.
Come to think of the 4 winning positions, i believe between 2 gd players, planning to move into the spaces is using the 3 types of pieces can be crucial. For eg, a triangle can only move diagonally, if both players are 1 space away from victory but red has a triangle in the entry square but unluckily has another piece in a diagonal position, he has to use another or perphaps a few more turns to move his 3 other winning pieces about to make space for this triangle as it is not allowed to move outside the entry space anymore. This can be really tricky now that i think abt it. Wow...