Well since they are in the ground water from rain or snow can get to them so only way to be sure they will work properly is to replace them. I don't mess around with damaged electrical wires especially since outer covering has been cut & electrical tape could let moisture seep in sooner or later.

A repair that will last can be done, but it is going to take heat shrink solder splices (they are used on aircraft they work so well).

The problem is that the typical repair, crimp splices and electrical tape, are very likely to fail when water gets into the repair.

Since they are paying for the work, demand the line be replaced by a contractor of your choosing.

I wouldn't trust a cable person that can't tell the difference between coax and LVT (or whatever type of wire the sprinklers use) and not one who cuts wires they don't know.

I would insist on them engaging someone to pull new wire. Ask for an escalation to a supervisor etc if necessary (but be nice about it of course)

agrred the guy was a dolt for cutting wires that had no relation to cable and should have been recognized as such pretty easily. You can ask for replacement, but realistically if there is enough exposed wire on both side of the cut the wires can be spliced and protected for the long term. Just make sure they use a waterproof splice kit that incorporates a good coating. Don't let them just twist the leads together and wrap it with electrical tape.

If you really want to get fancy have them put the plaice inside a weatherproof junction box.

If the leads can be replaced without having to expose the entire wire run and can be easily pulled through a conduit, then go for the replacement.

If everything has to be dug up then a splice is good.

these lines are low voltage and not a huge safety concern, but you want to make sure the connection lasts.

Here is a link that might be useful: direct bury splicing products from 3M