For point of reference, assume Tweety is in a window in the front face of the building. When the building is first shown, the fire escape stairs would be on the left side of the building (as viewed from the front). When Sylvester climbs the stairs, he goes around two corners to get to Tweety (whereupon he slips on the banana peel). Since Sylvester had to go around two corners, that would indicate that the fire escape stairs were on the back side of the building, not the left side as initially shown.
The building where the gangsters are hiding out is shown with Tweety in the top floor window, and the fire escape stairs just around the corner. When Tweety says, "Look at that nice putty tat trying to save me!", Sylvester had not turned the corner yet, so he wouldn't be visible from Tweety's vantage point.