This is a multifaceted question. While I cannot give a "correct" answer, as there really isn't one here, I can outline two different potential views on the issue.
There are plenty of reasons to believe that prisoners should be able to use JPay. We can look at the Eighth Amendment here. While not being able to use video chat or receive money may not seem like cruel and unusual punishment, being forced into a rough economic or social situation could be considered this way. Also, the Eighth Amendment requires that prisoners get a minimum standard of living. You may consider contact with your loved ones as part of this minimum standard, in which case being able to use JPay may be the only way to reach this standard.
A counterargument to this could be a more thorough look at the rights prisoners are given in jail. While Cornell Law finds that "[p]risoners also have rights to speech and religion, to the extent these rights do not interfere with their status as inmates," being deprived of JPay video chat and money exchange does not really constitute a free speech violation. JPay could also be argued to be a luxury, and nowhere in our laws is it specifically stated that prison inmates have the right to anything like the JPay services. In this view, one would think that those in corrective facilities have done their crime and must pay for it, and they must sacrifice certain luxuries or things that make life more enjoyable or convenient.