Tiling to Island Mount Bath

I am about to start tiling my bathroom, after having renovated the rooms completely.
I have a bath that has an island mount, where the edges of the bath are 100mm from the wall, with a horizontal surface between the bath and walls.
i am going to continue the floor tiles up the side, and across the top to surround the bath.
My question is, should i tile to the edge of the bath and seal it, or should i tile UNDER the edge of the bath, and effectively have the edge of the bat sitting on top of the tiles, and then seal it?
i.e should i install the bath then tile up to the edge, or should i tile to the cutout for the bath, and then lower the bath down on top of the tiles afterwards. both ways obviously i will seal the edges.

the bath is supported from below, so it wont be actually 'hanging' from the tiles and there will be no weight actually on the tiles.

so what does everyone think?

Thanks in advance for any replies!

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should i tile to the edge of the bath and seal it

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No

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should i tile UNDER the edge of the bath, and effectively have the edge of the bat sitting on top of the tiles, and then seal it?

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Yes

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should i tile to the cutout for the bath, and then lower the bath down on top of the tiles afterwards.

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Yes

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the bath is supported from below, so it wont be actually 'hanging' from the tiles and there will be no weight actually on the tiles.

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I agree this is the way it should be.

On my hob I waterproofed the walls adjoining the bath to the height of 300mm(no shower involved) and waterprooofed the whole hob. I used silicone to seal the wall to hob and hob to floor screed joins .I then embedded reinforcing tape in the membrane at the joint between the hob and the wall and hob to floor. I figure that water will eventually spill over the top of the hob due to cleaning or whatever.