Voicemail - notification vs. text msg

Hello - This may be a carrier issue, but I thought I would try this as well ...

iPhone 4 - voicemail comes in and a little red dot/number comes up on the phone icon to indicate I have voicemail - perfect. 🙂

I just purchased an iphone 5 with a new carrier - voicemail comes in & I recieve a text message to let me know that I have a voicemail. I would much perfer it to go to the icon. Does anyone know how I can make this happen? I was told I had to purchase a Visual Voicemail Plan (???)