If you understand the design of a properly built shower, you'd realize it isn't built properly and that neither the tile nor the grout will prevent this from happening, or continuing to happen, but just slow it down.
In a properly constructed shower, there are four layers to a shower pan:
1. a presloped layer of deck mud (sloped towards the drain)
2. a waterproof liner (it needs to be sloped so water can drain out)
3. another layer of deck mud to give you something tile will stick to
4. the tile on the floor.
The pan liner attaches to the clamping drain and makes a waterproof shield. There are some small slots or holes in the drain (called weepholes) that allow any water that gets under the tile (it will, regardless of what you do) can drain out. If those are blocked (fairly common) or the liner is installed flat on the floor (even more common), your pan will eventually fill up with stagnent water; nothing you can do about it but rebuilt it properly or live with it.
Check out www.johnbridge.com for help on fixing your shower.