+1 Hello Cheeto, and Welcome to TFP,
Congratulations on your soon to be delivered Hot tub.
It sounds as though you are using one of recommended test kits for your testing, which is great.
Yes a 240ppm TA on the fill water can in fact be correct. Once you get your hot tub with your fill TA being high to start, and your pH already at the higher end at 7.8ppm, you will most likely at 1st be battling a increasing pH level, until you can get the TA level down enough so it can stabilize the pH better, but not to worry we can help you do that when the time comes.
Here is a link that might help explain what we may be asking you to do at that time should the pH start increasing, as I suspect it will do because of the high TA and a starting pH of 7.8ppm.
http://www.troublefreepool.com/threads/3134-High-pH-That-will-just-NOT-come-down
http://www.troublefreepool.com/content/129-how-to-lower-lowering-total-alkalinity
Here are a few more links on other important topics that you can look over before your Hot Tub arrives.
http://www.troublefreepool.com/content/123-abc-of-pool-water-chemistry
www.troublefreepool.com/content/139-recommended-pool-chemicals
http://www.troublefreepool.com/content/134-recommended-levels
http://www.troublefreepool.com/content/114-poolmath-pool-calculator
Once your Hot Tub arrives and you are able to recheck your levels so we know everything that is occurring we can certainly assist you more from there.
Also once your Hot Tub arrives Please fill in your Signature information (or If you know the size etc. you may fill some of that in there now, along with your test kit information then add to it should you need to later.
This can be done by: Going to the top of this page Clicking on Forum Actions---->General Settings and then look down the left side of your screen for a Bold tab called MY SETTINGS, and EDIT SIGNATURE is located there.
Here is a link describing the type of information you can add to it so we can better assist you.
http://www.troublefreepool.com/content/115-read-before-you-post
I hope this helps. Again welcome to TFP.
Feel free to post any other questions you may have, and someone will be happy to assist. Have a wonderful Day