Finishing with silicone gives a water-resistant seal and a good silicone accounts for movement and temperature changes (e.g. when you have a hot shower). Usually, you can get silicones from the same manufacturer as the grout in a matching colour, so you shouldn't get an obvious line of silicone and it gives a nice neat finish.

Silicone is a must between junctions to accommodate any movement(Grout will crack) only an amateur would use grout in this situation. There are alternatives made by Schluter Systems for wall/floor junctions. Link below:

http://www.schluter.co.uk/movement_joints.aspx

May i also add that i hope the silicone used is neutral curing, as normal(acetoxy) silicone releases acetic acid when curing and will attack natural stone & cause bleeding along the edges.

Agree with the Silicone, however, obviously this should not be between tiles, it goes around the edges to stop water where it's harder to get grout right in, and to stop water ingress under baths, down the edges of baths, at the back of sinks around showers etc.

Some of the pics look like you have silicone in between tiles where it should be just grout.

Re:- The beading - If you're going to have beading, it has to be right along the stairs not just one part of it. I suspect, that the walls were not quite level, ( they never are ), so to combat this, they've put a bead on, but it needs continuing up the stairs.

You also should not be able to see screw heads like that. Looks like round head screws have been used. Wood screws are flat on top and pull in to the wood, then you come along with a little bit of caulk . filler, hid the screw heads and paint. They need to change them, looks terrible.

A movement joint should of been used across the door threshold.

As Traditional Sash Windows says:-

Movement Joints......Why, Where, When

I have never used anything other than flexible tile grout and flexible tile adhesive. I have also never heard of using silicone between tile joints instead of grout. I can't see the strip, it's not visible, usually looks like a little strip / bar running through the centre of two tiles. The reason it looks awful is because of the way they've chosen to cut and lay the tiles.

Get someone in for a second opinion? Maybe they'd listen to someone else? Don't know what else to say.