How can I hold the flavor and texture of my spheres?
Once the calcium and alginate react the process will continue regardless of whether you rinse them or not. The rinsing will slow the process down but won't inhibit the reaction altogether. In order to ensure liquid centers you will have to heat the spheres to 85°C for 10 minutes (from modernist cuisine). However, you have a ton of calcium going on in your mix between the calcium in the apple juice and the fact that you're using calcium lactate as your setting bath so you are likely going to benefit from a sequesterant like sodium citrate to bind up some of the free calcium ions. I would actually suggest you go with a calcium chloride bath for this type of direct spherification. If you were doing larger spheres I would suggest reverse spherification but that won't do you any good for caviar.