There's supposed to be a gap between the tiles and the shower pan. It's so water doesn't crawl up behind the tiles from the hydrostatic pressure. That's not your problem. If you're getting a leak downstairs, it's probably from around the drain or the membrane behind the tile where it meets the floor. Tile grout isn't waterproof. It's porous. Your problem is with the layer that's actually meant to be waterproof.