I've demolished a lot over the years, if it were me I'd bust it up, remove it completely and do it right otherwise years from now your wanting to do something there and someone left the darn thing in the way, right now on my own house they used the cystern wall on one side for the house wall, so if I'm wanting to add onto the house on that side, I need to start over agian and tear it all out, as to why, I'm wanting to put an attached garage on that end of the house and it'll be in the center of the garage.
As for tiling it out, done that too, cement is porous and will fill to the level of the water table if its not tiled out, unless they used something to line the inside of it, but as old as it is it'll still leak water in and out, also even with tile and filled in it'll hold water, there is less pressure inside the tank than the ground outside the tank and water will fill inside it and around the rock, works like a wick in a lamp to a certain extent. Once you've got the hole knocked in the bottom and the top knocked in, just dig it out completely and backfill with good fill dirt nows the time to do it with equipment, after the addition is on its all done by hand, I know I've had to put new sewer lines in under a house addition one time and someone left the cement fill in there, cussed more on that job than I've done on all jobs I've ever done, ten minutes with backhoe would have saved me a week doing it by hand under an addition or house with a crawl space.
A friend of mine had an old hog building with a pit in it he burned down, long story short, he said he'd never build there with anyhting, we buried the pit and all cement there in the pit and two years later he wanted his new house on the spot we buried the pit, luckily we buried it deep enough he could put a house with a crawl space under it there, just had pillars going down till it hit the cement we buried, worked great, now the mice and rats live it the voids of the cement we buried and have a roof over their heads to keep the rain out of the holes, literally there is mice and rats living under the house in the debris we buried, I tried to tell him not to do it there but to put it elsewhere or dig it all out before building but he saved money by doing it his way, now he can spend the rest of his life trying to figure out how to get and keep critters out from under his new house and lving in the voids in the old hog pit cement we buried, not to mention the rats have eaten into the sewer lines that we buried under the end of the house that go to the septic tank and the rats have the place undermined so badly they get inside the plastic pipes and into his house up through the toilet, not that they don't get in anywhere they want to, but it creeped out his wife, we have never told her just how this all came about yet, she hasn't figured it all out yet and hopefully never will or else he's going to have to sell his property, we just tell her its a fluke and won't happen again, so far she's buying it, but from here on out I'm not crawling under his house ever again for anything, I've been greeted in the eye with too many rats under there for me to ever go back under it again. Any time you bury some cement or debris there are voids in the dirt and debris for critters to live, unless its dug out completely and refilled with good fill you never eliminate this problem, seen it many times and will never again bury anything beside anyone's house, least of all my own, especially septic tanks and lines to septic tanks that are abandoned once a new system is put in place, cistens are the second worst thing to contend with in my book. Just tossing out some experiences I've had, do as you wish.