Is the exposed strip ok or should it be protected?

They can be left like that; however if you look for a type of diffuser to go over them it may help soften the shadows it makes in the current location. You'll need to check for which diffusers can be be installed over your lights. Check out Environmental Lights for a few options.

Mine is in the same place to the front. It works and you do not see the strips when sitting. It lights up the back of the counter. If I want to light up the front of the counter I use the overhead lights.
I think this is how all of them are supposed to be installed.

yes, they should be up front or they would be just illuminating your backsplash.

What do you mean that they are exposed? If you didn't get a bar, but string LEDs they will not have a diffuser cover. Did you not discuss what type of lights were going to be installed? Yes, these are strip lights. Obviously this isn't what you were expecting, but if you didn't specify or discuss what you wanted, the installer is going to put anything up that's cheap for them to purchase.

This was a last-minute decision, my contractor recommended changing them while the electrician was already at my house...and it was changed right away, I wasn't asked and didn't have time to research unfortunately. If the way this is done is considered standard then I'm fine with it, I just wasn't sure. We've had so many issues with this reno I don't know what's right anymore...

Yes, string lights look like that, but not everyone prefers them, do to the glare they create on the counter and they are also cheapest thing you can buy. Unless they made some very complicated hard wiring, you can easily changes these out for something you like better later.

Good to read threads that are Consumer Guide: info on what to expect and on new products [to some including me]..... good 'luck'.....