Yes - all of the ethernet wall jacks should terminate in a patch panel which may be the mentioned "wall panel" in the master bedroom closet. Google "patch panel images" and you will find many patch panel images. Lots of variations but the concept is the same.
There should be a wire (hopefully labeled) going from the patch panel to each ethernet wall jack.
Then each port on the patch panel is connected either directly to a router LAN port or a switch if the router does not have enough ports.
Here is a link as a reference:
https://www.google.com/search?q=patch+panel+image&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiMzIPr4bDQAhUK4SYKHWQLDXcQ_AUICCgB&biw=1600&bih=783#tbm=isch&q=patch+panel+and+switch+images&imgrc=BQbzRark7OuxTM%3A
There are many other such links, diagrams, images available. Even some "How to" tutorials if you are so interested.
Note: And you will need at least one wall outlet for power connections. Ventilation is important so the closet space does not get too warm.
As for the routers hold until TWC/Spectrum gets things up and running with what you have. One reason is that if you make changes afterwards then you will at least know that what they set up works. If you do something and things do not work then you can roll back the change and "regroup".
Be very certain that everything they do does work before the tech(s) leave. Get any promises in writing and get a receipt with a serial number for any thing they take back.
The other part of the matter is that the ISP may only support certain products. All too easy for them to blame your gear if something does not work.
I do recommend that you go online and see if you can find the User Guide/Manual for the CellSpot router. The manual should give you some sense of what needs to be done and how to do that. Easy to again google for more information as you deem necessary and appropriate. I.e., diagrams, manufacturer FAQs and forums. Look for some reviews by verified purchasers.
The other factor to be aware of is since it is a new home there is a good chance that the existing ethernet wiring may have problems. Could be copper clad aluminum or older Cat 3 cabling. Poor terminations, improper cable runs, staples embedded in the wire; all sorts of problems if the installer did not know (or care) about how infrastructure should be done. May not have tested the connections even.... A loose connection will wreak havoc - sometimes working sometimes not.
Take a close look at everything you can. Sketch out a diagram. Note cable labels, makes & models, Open a wall jack in each room to see what you can find. You will be much more comfortable with it all after some "hands on".
So the idea is to start simple, plan out what needs to be done, and then work methodically through it all.