I built something similar for watering chickens. In their case I used drinker cups fed from a reservoir of water about 3 feet higher than the cups. I needed some automatic method of maintaining the reservoir filled. Sounds a lot like the tank on a toilet, doesn't it..? (photo: www.dhgate.com)
So I built a miniature replica of a toilet tank from a pantry food storage container just large enough to hold a toilet float valve! (photos: www.homedepot.com, www.rubbermaid.com)
Drill a hole in the bottom of the storage container; install the float valve. Use normal plumbing parts to supply the float valve: a riser tube or hookup hose, a shutoff valve, etc. In my case I drilled another hole in the storage container and installed a bulkhead fitting to create the port for drawing water down to the drinker cups.
I don't know whether a tortoise can be trained or is physically capable to activate a drinker cup or not -- chickens just figure it out on their own. You're absolutely right that you could set the reservoir so that its height and the heights of the bowls match, then connect them with tubing below the water line.
In a comment you mentioned a one-way ("check") valve. Perhaps you can build one from a chicken drinker valve with a fishing float glued to it, and possibly some fishing weights too. Set it so that the weights make the drinker valve sink, allowing water flow until the buoyancy of the float on the rising water counteracts the weights and closes the valve. Put a stopper above the float -- otherwise if the bowl overfills the float will rise too much, opening the valve, and causing endless overflow!