I have a Lumia 620 on Cricket and visual voicemail worked from when I got the phone (March-April 2014) until about July. Since that time only standard voicemail has been available. However, my situation is complicated by the fact that I flashed Lumia Cyan / WP 8.1 and sim-unlocked the device prior to the disappearance of visual voicemail.
I spoke with Cricket today and I was also told that I "need to download the VVM app". After I educated the customer service rep that Windows Phone has built-in VVM functionality and doesn't require an app, I asked to speak with his supervisor (whom I had hoped would be more knowledgeable). Unfortunately, the supervisor was also insistent that I needed to download an app or that the problem was with my phone.
I was subsequently forwarded to Nokia support, who confirmed that, regardless of firmware or sim-lock status, any Lumia will have built-in VVM capability. Furthermore, the Nokia rep told me that VVM requires implementation by the carrier on their systems.
So, I called Cricket back and informed them of Nokia's response. Since the people answering calls at Cricket customer support lack the technical knowledge to deal with this issue they opened a case for their technical support to investigate further.
I'm really not sure what to make of the VVM situation on Cricket, but I have not been impressed with their tier one support. I know that my sim-locked 620 with Amber firmware used to have VVM functionality and that my sim-unlocked Lumia 521 with Black firmware (which had VVM functionality on T-Mobile) both lack VVM now when using my Cricket sim. I was told that the technical support case should be resolved in the next 5 days, so I will report back when I have updated information.