It sounds like a makeshift process was used to put the toilet in the shower.
One solution would be to put a vertical flange around the hole in the shower pan that rises higher than the shower drain.
1. Remove toilet.
2. Check the bottom of the toilet to determine where a vertical flange can be installed to clear the underside of the china. Make a pattern and test fit.
3. Form a metal flange that can be attached to the pan with rivets and/or solder, and fasten it to the pan with a PERMANENT waterPROOF seal. The top of the flange should be at least 1/2 inch above the top of the tile floor of the shower.
4. Install tile as in the shower, or very good concrete grout, a little higher than the existing shower floor but still clearing the china of the toilet, all the way to the new vertical flange, so the water doesn't stand around the flange. Grout or seal the pan VERY WELL.
5. Be sure that you seal the area where the toilet is bolted down. There must be NO PATH from the shower to the floor.
6. Pour some water in the shower, and if it is done right, it will be completely contained in the shower pan until it runs down the shower drain. It is completely isolated from the toilet drain and from the floor area immediately adjacent to the toilet flange. The dam should be independent of the toilet because the toilet may move a bit and break any seal that you install between the toilet and the shower floor.
7. Reinstall the toilet.
You could use some other means to make a dam around the hole in the pan, under the toilet, but the effectiveness of the solution will depend on damming the water from the shower to keep it in the shower pan. It should include some kind of mechanical fastening and sealing of a waterproof solid part. I suppose you could get two wax rings and cut/form them to make a bigger one to make the dam, but I wouldn't rely on that.
If you paid a professional to do the job in the first place, he should come fix it permanently for no additional charge.