Tar paper is not waterproof. It has a fairly high and variable perm rating, so moisture vapor can pass through it. It'll shed liquid water, but if inundated, it can saturate and liquid moisture can wick through it.

It's often used behind floated mud walls. So if lathe and mud are going over this, then in this application it would be perfectly appropriate.

As a drainage plane behind tiled cement board in showers, for example, in my region (New England), tar paper fell out of favor...25-30 years ago?

For the past 15-20 years it's almost all been surface applied membranes where I live. Liquids like Hydroban and RedGard, or sheets like Kerdi, or now, USG systems.

When house construction tightened up over the past few decades, it made sense to tighten up moisture and control it at the sources. Bathroom moisture control became more important. As did control of moisture generated when cooking.

Ask your installer what other specific building materials will be going on the walls. Your building department may be able to assist you with information specific to your location.

Agree w/MongoCT

Jumbotex and aquabar are still the norm/used in CA under chicken or 2.5 lath. Theyve lapped the sheets shingle style and you are getting a common CA hot mop mud job. Likely youll be just fine.

If you want to get nit-picky start demanding they put a preslope UNDER the hot mop pan and verify it drains with a flood test.. That is the biggest/common failure in the CA hotmop.