I called and asked about this offer. In Tampa, they will give you a 6-month promo price in addition to upgrading you to Turbo or Turbo Plus. They made it sound like for the first six months, you'll basically be paying about the current price for the standard speed.... then afterwards it will be the regular price + about $10 or $15 dollars. This offer may exist in other BHN service areas as well, like Orlando. Depending on what modem you have now, they may say that you'll have to wait for a modem swap before you can support the higher speeds and get the upgrade.
Also some CSRs aren't "aware" of what is going on, so you might be told you can't get this without having "Digital Phone" service because of the equipment they believe is required for the 20 meg speed to be deliverable to you. As far as I'm aware, it's actually just a DOCSIS compatibility thing, so if you have a recent DOCSIS modem as far as standards, they should just be able to push this upgrade to you via bin file when the modem is next power-cycled....which they can typically do from there end as well.