Without photos it's not easy to say but from the description it would seem that, yes, you will need to install a door if you want to keep water splashing out onto the surrounding floor.

Is this curbless? If do, it is likely built incorrectly, and is too small.

Post a whole lot of pictues. Ones from the beginning through the build process, to now. And post the floorplan that your designer came up with for this.

Get a narrower shower head if the problem is overspray.

A Silcon sealing strip might work for you. Sometihing like this

I don't know if I would order anything from Alibaba but here is the link for info...mayb find something like it on Amazon or something.

https://www.alibaba.com/product-detail/Customized-Translucent-Half-Round-Kitchen-Sink_1601229996827.html?spm=a2700.7724857.0.0.6caa1b854qecDu

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Where did you think the water would go? No door means nothing to stop the water and if no sill then the room becomes a wet room, nothing to stop water which goes everywhere.

The pictures of this disaster are........where? :

Show us pics and size of shower and openings. Does it go on the floor beyond your bath matt? Can a good thick mat take care of the problem? Is it a light spray escaping or massive amounts of water?

Can you angle the head differently so you stand in a different spot and the water splashes off of you to a different part of the shower?

Many factors in what sounds like a poorly planned shower.

If you "just replaced" a standard tub shower with a curbless shower, then it isn't big enough to not have splash out. The slope should extend into the room, and the room floor should be waterproofed. Sounds like you hired the cheapest BS artist.

Op came back three days ago and posted an exclamation mark. Maybe they meant to post photos? Seems senseless to keep commenting until they can do that…

" Seems senseless to keep commenting until they can do that… "

Exactly. Until then it is mostly ridiculous disaster filled assumptions.